Mathematische Nachrichten最新文献

{"title":"On p-Numerical Radius Inequalities for Hilbert Space Operators","authors":"Fugen Gao, Mengyu Hou, Jie Zhao","doi":"10.1002/mana.70187","DOIUrl":"https://doi.org/10.1002/mana.70187","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper introduces novel inequalities for the <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-numerical radius of operators. Among our main findings, we prove that\u0000\u0000 </p><div><span><span><!--FIGURE--><span></span><math>\u0000 <semantics>\u0000 <mtable>\u0000 <mtr>\u0000 <mtd>\u0000 <mrow>\u0000 <msub>\u0000 <mi>w</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <mfenced>\u0000 <mi>T</mi>\u0000 </mfenced>\u0000 <mo>≤</mo>\u0000 <msup>\u0000 <mn>2</mn>\u0000 <mrow>\u0000 <mfrac>\u0000 <mn>1</mn>\u0000 <mi>p</mi>\u0000 </mfrac>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <munder>\u0000 <mi>min</mi>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>∈</mo>\u0000 <mfenced>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 </munder>\u0000 <mfenced>\u0000 <msub>\u0000 <mi>w</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mover>\u0000 <mi>T</mi>\u0000 <mo>∼</mo>\u0000 </mover>\u0000 <mi>t</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 8","pages":"2191-2207"},"PeriodicalIF":1.0,"publicationDate":"2026-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148695963","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Uniqueness for Neumann Problems for Nonlinear Elliptic Equations With Lower Order Terms","authors":"Maria Francesca Betta,&nbsp;Olivier Guibé,&nbsp;Anna Mercaldo,&nbsp;Maria Rosaria Posteraro","doi":"10.1002/mana.70175","DOIUrl":"https://doi.org/10.1002/mana.70175","url":null,"abstract":"<p>In this paper, we prove uniqueness results for weak solutions to a class of Neumann problems, whose prototype is \u0000\u0000 </p><p>Uniqueness results for weak solutions are proved under smallness assumptions on the coefficients <span></span><math>\u0000 <semantics>\u0000 <mi>b</mi>\u0000 <annotation>$b$</annotation>\u0000 </semantics></math> or <span></span><math>\u0000 <semantics>\u0000 <mi>c</mi>\u0000 <annotation>$c$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 8","pages":"1956-1982"},"PeriodicalIF":1.0,"publicationDate":"2026-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70175","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148695844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Approximate Solutions With Convergence Results for Optimal Control Problems Driven by Generalized Multiobjective Games With Application to Walrasian General Equilibrium","authors":"Nguyen Van Hung,&nbsp;Andre A. Keller,&nbsp;Jen Chih Yao","doi":"10.1002/mana.70179","DOIUrl":"https://doi.org/10.1002/mana.70179","url":null,"abstract":"<div>\u0000 \u0000 <p>The purpose of this paper is to establish convergence results of the approximate solutions for control systems of generalized multiobjective games and optimal control problems driven by generalized multiobjective games. First, we revisit the control systems of generalized multiobjective games. Then, using a sequence of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>Γ</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$Gamma ^n$</annotation>\u0000 </semantics></math>-converging mappings, we establish the upper convergence, lower convergence and convergence of the solution sets for such problems. Second, we investigate sufficient conditions for the convergence of approximate solutions to optimal control problems. Finally, as a real-world application, we consider the special case of control systems of economic equilibrium models. The results presented in the paper are new and improve some of the main results given in the literature.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 8","pages":"2063-2086"},"PeriodicalIF":1.0,"publicationDate":"2026-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148696497","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability for the Two-Dimensional Boussinesq Equations With Fractional Horizontal Dissipation and Thermal Diffusion","authors":"Qunyi Bie,&nbsp;Jiatong Yu,&nbsp;Yanping Zhou","doi":"10.1002/mana.70184","DOIUrl":"https://doi.org/10.1002/mana.70184","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we focus on the stability of perturbation near a steady state of the two-dimensional (2D) Boussinesq system with fractional horizontal dissipation and thermal diffusion. In 2D full space <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$mathbb {R}^2$</annotation>\u0000 </semantics></math>, by virtue of the absence of vertical dissipation, the stability remains open in the Sobolev framework. When the domain is <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mo>×</mo>\u0000 <mi>R</mi>\u0000 </mrow>\u0000 <annotation>$mathbb {T}times mathbb {R}$</annotation>\u0000 </semantics></math>, where <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>T</mi>\u0000 <mo>=</mo>\u0000 <mo>[</mo>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>]</mo>\u0000 </mrow>\u0000 <annotation>$mathbb {T}=[0,1]$</annotation>\u0000 </semantics></math> is a periodic interval, we obtain the stability in the Sobolev space <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$H^2$</annotation>\u0000 </semantics></math>. Furthermore, in view of the presence of fractional operators, some of the standard energy estimate techniques no longer work. To overcome these difficulties, we resort to some new anisotropic interpolation inequalities and the strong Poincaré-type inequalities involving fractional derivatives. Moreover, the oscillatory part of the solution is proven to converge exponentially to zero in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$H^1$</annotation>\u0000 </semantics></math> as time goes to infinity. Our results extend some known ones and provide support for numerical simulation of Boussinesq equations with partial fractional dissipation.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 8","pages":"2139-2160"},"PeriodicalIF":1.0,"publicationDate":"2026-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148695787","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Relationship Between Limiting K-Spaces and J-Spaces in the Real Interpolation","authors":"Bohumír Opic,&nbsp;Manvi Grover","doi":"10.1002/mana.70159","DOIUrl":"https://doi.org/10.1002/mana.70159","url":null,"abstract":"&lt;p&gt;In the paper, “Description of the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;annotation&gt;$K$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-Spaces by Means of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;J&lt;/mi&gt;\u0000 &lt;annotation&gt;$J$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-Spaces and the Reverse Problem,” &lt;i&gt;Mathematische Nachrichten&lt;/i&gt; 296, no. 9 (2023), 4002–4031, we have established conditions under which the limiting &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;annotation&gt;$K$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;b&lt;/mi&gt;\u0000 &lt;mo&gt;;&lt;/mo&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$(X_0,X_1)_{0,q,b;K}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, involving a slowly varying function &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;b&lt;/mi&gt;\u0000 &lt;annotation&gt;$b$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, can be described by means of the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;J&lt;/mi&gt;\u0000 &lt;annotation&gt;$J$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-space &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mo&gt;;&lt;/mo&gt;\u0000 &lt;mi&gt;J&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$(X_0,X_1)_{0,q,a;J}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, with a convenient slowly varying funct","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 7","pages":"1556-1587"},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mana.70159","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148395183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Valuation Rings as Limits of Complete Intersection Rings","authors":"Dorin Popescu","doi":"10.1002/mana.70144","DOIUrl":"https://doi.org/10.1002/mana.70144","url":null,"abstract":"<div>\u0000 \u0000 <p>We show that a valuation ring containing its residue field of characteristic <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$p&gt;0$</annotation>\u0000 </semantics></math> is a filtered colimit of complete intersection <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>F</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>${bf F}_p$</annotation>\u0000 </semantics></math>-algebras.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 7","pages":"1517-1525"},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148395061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Pestov Identity on the Frame Bundle and Associated Homogeneous Fibrations","authors":"Mihajlo Cekić,&nbsp;Thibault Lefeuvre,&nbsp;Andrei Moroianu,&nbsp;Uwe Semmelmann","doi":"10.1002/mana.70167","DOIUrl":"https://doi.org/10.1002/mana.70167","url":null,"abstract":"<div>\u0000 \u0000 <p>We prove a global Pestov identity on the (orthonormal) frame bundle of a Riemannian manifold and deduce similar identities on associated homogeneous fibrations. As a particular example, this provides a concise proof of the Pestov identity on the unit tangent bundle of the manifold.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 7","pages":"1737-1750"},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148395117","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On Laguerre Isotropic Hypersurfaces","authors":"Fernanda Alves Caixeta,&nbsp;Keti Tenenblat","doi":"10.1002/mana.70162","DOIUrl":"https://doi.org/10.1002/mana.70162","url":null,"abstract":"<div>\u0000 \u0000 <p>We study Laguerre isotropic hypersurfaces in the Euclidean space, which are hypersurfaces whose Laguerre form is zero and the eigenvalues of the Laguerre tensor are constant and equal to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mo>≥</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$lambda ge 0$</annotation>\u0000 </semantics></math>. We prove a rigidity theorem for the L-isotropic hypersurfaces parameterized by lines of curvature. Moreover, we study the hypersurfaces that are L-isotropic and L-isoparametric simultaneously and we show that for such a hypersurface, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$lambda =0$</annotation>\u0000 </semantics></math>. We obtain necessary conditions for the existence of L-isotropic hypersurfaces with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>λ</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$lambda &gt; 0$</annotation>\u0000 </semantics></math> and we prove that a certain function, determined by the radii of curvature of the hypersurface, is bounded above by <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>λ</mi>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>${1}/{2lambda }$</annotation>\u0000 </semantics></math>.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 7","pages":"1596-1623"},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148395204","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Biconservative Weingarten Surfaces With Flat Normal Bundle in \u0000 \u0000 \u0000 \u0000 N\u0000 4\u0000 \u0000 \u0000 (\u0000 ε\u0000 )\u0000 \u0000 \u0000 $N^4 (epsilon)$","authors":"Stefan Andronic,&nbsp;Stefano Montaldo,&nbsp;Cezar Oniciuc,&nbsp;Antonio Sanna","doi":"10.1002/mana.70163","DOIUrl":"https://doi.org/10.1002/mana.70163","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we investigate the class of biconservative surfaces with non-constant mean curvature in four-dimensional space forms <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>N</mi>\u0000 <mn>4</mn>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>ε</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$N^4(epsilon)$</annotation>\u0000 </semantics></math>. Specifically, we focus on biconservative surfaces with non-parallel normalized mean curvature vector field (non-PNMC) that have flat normal bundle and are Weingarten. In our initial result, we obtain the compatibility conditions for this class of biconservative surfaces in terms of a first-order ordinary differential equation system. Subsequently, by prescribing the flat connection in the normal bundle, we prove an existence result for the considered class of biconservative surfaces. Furthermore, we determine all non-PNMC biconservative Weingarten surfaces with flat normal bundle that either exhibit a particular form of the shape operator in the direction of the mean curvature vector field or have constant Gaussian curvature <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>K</mi>\u0000 <mo>=</mo>\u0000 <mi>ε</mi>\u0000 </mrow>\u0000 <annotation>$K = epsilon$</annotation>\u0000 </semantics></math>. Finally, we prove that such surfaces cannot be biharmonic.</p></div>","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 7","pages":"1624-1664"},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148395009","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A New Class of Operators Related to Almost p-Limited Sets","authors":"Halimeh Ardakani,&nbsp;Vinícius C. C. Miranda","doi":"10.1002/mana.70169","DOIUrl":"https://doi.org/10.1002/mana.70169","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;This paper is devoted to the study of &lt;i&gt;almost&lt;/i&gt; &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;&lt;i&gt;-limited completely continuous&lt;/i&gt; (&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm a}p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-lcc) operators, a new class of operators naturally associated with the notion of almost &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-limited sets in Banach lattices. We provide necessary and sufficient conditions under which every positive operator dominated by an &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm a}p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-lcc operator is also &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm a}p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-lcc. In addition, we establish necessary conditions under which positive &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm a}p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-lcc operators admit &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm a}p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-lcc adjoints, and under which positive operators whose adjoints are &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm a}p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-lcc are themselves &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm a}p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-lcc. We also explore the connections between &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${rm a}p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-lcc operators and several well-known classes of operators, including AM-compact, &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;annotation&gt;$M$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-weakly compact, and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 ","PeriodicalId":49853,"journal":{"name":"Mathematische Nachrichten","volume":"299 7","pages":"1781-1794"},"PeriodicalIF":1.0,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148395068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}