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Advances in Operator Theory最新文献

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On operators commuting with a quasinilpotent operator of finite nullity and ascent 关于算子与有限零和有限上升的拟幂算子的可交换
IF 0.7
Advances in Operator Theory Pub Date : 2026-08-28 DOI: 10.1007/s43036-026-00534-5
Pietro Aiena, Miloš D. Cvetković
{"title":"On operators commuting with a quasinilpotent operator of finite nullity and ascent","authors":"Pietro Aiena,&nbsp;Miloš D. Cvetković","doi":"10.1007/s43036-026-00534-5","DOIUrl":"10.1007/s43036-026-00534-5","url":null,"abstract":"<div><p>Let <i>X</i> be an infinite-dimensional complex Banach space and let <i>L</i>(<i>X</i>) denote the algebra of all bounded linear operators on <i>X</i>. In this paper, we study the spectra arising from Fredholm theory and Weyl-type theorems of an operator <span>(T in L(X))</span> that commutes with a quasinilpotent operator <span>(Q in L(X))</span> satisfying <span>(alpha (Q)&lt;infty )</span> and <span>(p(Q)&lt;infty )</span>, where <span>(alpha (Q))</span> and <i>p</i>(<i>Q</i>) denote the nullity and the ascent of <i>Q</i>, respectively.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148838397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Factorization of anti-linear and C-normal operators 反线性和c -正规算子的分解
IF 0.7
Advances in Operator Theory Pub Date : 2026-08-27 DOI: 10.1007/s43036-026-00533-6
Sudip Ranjan Bhuia
{"title":"Factorization of anti-linear and C-normal operators","authors":"Sudip Ranjan Bhuia","doi":"10.1007/s43036-026-00533-6","DOIUrl":"10.1007/s43036-026-00533-6","url":null,"abstract":"<div><p>A conjugation <i>C</i> is an anti-linear isometric involution on a complex Hilbert space <span>(mathcal {H})</span>, and an operator <span>(Tin mathcal {B}(mathcal {H}))</span> is called <i>C</i>-normal if <span>(T^*T=CTT^*C)</span>. We develop a unified factorization framework around conjugations. First, applying Douglas’ theorem, we obtain a range-inclusion and factorization theorem for anti-linear operators and, as a corollary, a polar decomposition for anti-linear maps. Next, we present a factorization of <i>C</i>-normal operators based on the <i>C</i>-polar form. We then revisit the Cartesian decomposition <span>(T=A+iB)</span> (with <i>A</i> <i>C</i>-symmetric and <i>B</i> <i>C</i>-skew-symmetric) and give streamlined criteria and consequences. <i>In particular, we characterize</i> <i>C</i><i>-hyponormality via this Cartesian decomposition:</i> <i>T</i> <i>is</i> <i>C</i><i>-hyponormal if and only if</i> <span>(B^{*}Age A^{*}B)</span>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148838383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Jump type problems for inframonogenic functions on domains with fractal boundaries 分形边界域上次致函数的跳跃型问题
IF 0.7
Advances in Operator Theory Pub Date : 2026-08-18 DOI: 10.1007/s43036-026-00529-2
Carlos Daniel Tamayo Castro
{"title":"Jump type problems for inframonogenic functions on domains with fractal boundaries","authors":"Carlos Daniel Tamayo Castro","doi":"10.1007/s43036-026-00529-2","DOIUrl":"10.1007/s43036-026-00529-2","url":null,"abstract":"<div><p>This paper aims to study jump-type problems for inframonogenic functions on domains of the Euclidean space, <span>(mathbb {R}^{n},)</span> where <span>(n &gt; 2,)</span> with fractal boundaries, and with values in a Clifford algebra, where data functions are in higher-order Lipschitz classes. The main geometric tool is a high-dimensional version of the Refined Marcinkiewicz Exponent, which constitutes a local refinement of the Absolute Marcinkiewicz Exponent, a metric characteristic of fractal boundaries. A solvability condition is obtained, based on some properties of a suitable inframonogenic Teodorescu-type transform in Clifford analysis. It has been proven that utilizing this metric characteristic yields better results for studying these boundary value problems than using the Minkowski dimension or the Absolute Marcinkiewicz Exponent. An example is presented where the use of this new condition is the only viable solution to the problem.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782990","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multipliers between model spaces in non-Hilbertian setups 非希尔伯特设置中模型空间之间的乘数
IF 0.7
Advances in Operator Theory Pub Date : 2026-08-18 DOI: 10.1007/s43036-026-00531-8
Arun Kumar Bhardwaj, Arup Chattopadhyay, R. K. Srivastava
{"title":"Multipliers between model spaces in non-Hilbertian setups","authors":"Arun Kumar Bhardwaj,&nbsp;Arup Chattopadhyay,&nbsp;R. K. Srivastava","doi":"10.1007/s43036-026-00531-8","DOIUrl":"10.1007/s43036-026-00531-8","url":null,"abstract":"<div><p>Given a pair of inner functions <span>(Theta _1)</span> and <span>(Theta _2)</span> on the unit disk, and the corresponding inner functions <span>(I_1)</span> and <span>(I_2)</span> on the upper half-plane, the spaces of multipliers <span>(mathcal {M}^p(Theta _1, Theta _2))</span> and <span>(mathcal {M}^p(I_1, I_2))</span> between the corresponding model spaces have been studied. In contrast to the result <span>(mathcal {U}_infty mathcal {M}^2(Theta _1, Theta _2) = mathcal {M}^2(I_1, I_2))</span> obtained by Fricain, Hartmann, and Ross, we prove that this identity fails to hold if <span>(p ne 2)</span>. Furthermore, inspired by Crofoot’s work on surjective multipliers, we provide refined characterizations and new insights into the conditions under which equalities such as <span>(mathcal {M}^p(Theta _1, Theta _3) = mathcal {M}^p(Theta _2, Theta _3))</span> and <span>(mathcal {M}^p(Theta _1, Theta _2) = mathcal {M}^p(Theta _1, Theta _3))</span> hold.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Dynamics of weighted shifts on generalized Hardy spaces of trees 广义Hardy树空间上的权移动力学
IF 0.7
Advances in Operator Theory Pub Date : 2026-08-17 DOI: 10.1007/s43036-026-00530-9
Xiang Chen, Li Zhang, Zehua Zhou
{"title":"Dynamics of weighted shifts on generalized Hardy spaces of trees","authors":"Xiang Chen,&nbsp;Li Zhang,&nbsp;Zehua Zhou","doi":"10.1007/s43036-026-00530-9","DOIUrl":"10.1007/s43036-026-00530-9","url":null,"abstract":"<div><p>In this paper, we study the dynamical properties of weighted backward shifts <span>(B_{lambda })</span> on the little generalized Hardy space on a rooted tree. More precisely, we provide a characterization of <span>(mathcal {F})</span>-transitivity for <span>(B_{lambda })</span>. In addition, we characterize weighted backward shifts on rooted directed trees that have an orbit with a nonzero limit point. Using these equivalent conditions, we construct several concrete examples illustrating different dynamical behaviors of weighted backward shifts.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The Fourier transform in variable exponent Lebesgue spaces 变指数勒贝格空间中的傅里叶变换
IF 0.7
Advances in Operator Theory Pub Date : 2026-08-13 DOI: 10.1007/s43036-026-00526-5
André Pedroso Kowacs, Wagner Augusto Almeida de Moraes
{"title":"The Fourier transform in variable exponent Lebesgue spaces","authors":"André Pedroso Kowacs,&nbsp;Wagner Augusto Almeida de Moraes","doi":"10.1007/s43036-026-00526-5","DOIUrl":"10.1007/s43036-026-00526-5","url":null,"abstract":"<div><p>In this work we define a Fourier transform for each <span>(fin L^{p(cdot )}({{,mathrm{mathbb {R}},}}))</span>, for a large class of exponent functions <span>(p(cdot ))</span>, as the distributional derivative of a Hölder continuous function. A norm is defined in the space of such Fourier transforms so that it is isometrically isomorphic to <span>(L^{p(cdot )}({{,mathrm{mathbb {R}},}}))</span>. We also prove several properties of this Fourier transform, such as inversion in norm and an exchange theorem.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-026-00526-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148752025","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The numerical ranges of the generalized quadratic operators 广义二次算子的数值范围
IF 0.7
Advances in Operator Theory Pub Date : 2026-08-12 DOI: 10.1007/s43036-026-00525-6
Kangjian Wu, Qingxiang Xu
{"title":"The numerical ranges of the generalized quadratic operators","authors":"Kangjian Wu,&nbsp;Qingxiang Xu","doi":"10.1007/s43036-026-00525-6","DOIUrl":"10.1007/s43036-026-00525-6","url":null,"abstract":"<div><p>We investigate the generalized quadratic operator defined by </p><div><div><span>$$ T =left( begin{array}{cc} a I_H &amp; A c A^* &amp; bI_K end{array} right) ,$$</span></div></div><p>where <i>H</i> and <i>K</i> are Hilbert spaces, <span>(A:Krightarrow H)</span> is a bounded linear operator, <span>(I_H)</span> and <span>(I_K)</span> denote the identity operators on <i>H</i> and <i>K</i>, respectively, and <i>a</i>, <i>b</i>, <i>c</i> are complex numbers. It is shown that <i>T</i> attains its norm if and only if <i>A</i> attains its norm. Furthermore, a complete characterization of the numerical range of <i>T</i> is provided by a new approach.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751790","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fredholm operators on Hilbert modules Hilbert模上的Fredholm算子
IF 0.7
Advances in Operator Theory Pub Date : 2026-08-10 DOI: 10.1007/s43036-026-00528-3
Palanivel Manoharan
{"title":"Fredholm operators on Hilbert modules","authors":"Palanivel Manoharan","doi":"10.1007/s43036-026-00528-3","DOIUrl":"10.1007/s43036-026-00528-3","url":null,"abstract":"<div><p>Let A be a unital not necessarily commutative C*-algebra. In this manuscript, we define that a bounded adjointable operator between two Hilbert A-modules is a Fredholm operator if it has finitely generated projective kernel and cokernel as a straight forward generalization of the classical definition. We generalize the classical Atkinson theorem and a version of Atiyah–Janich theorem to show that the index holds the homotopy invariance property for this class of operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-026-00528-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Wold-type decomposition and Beurling-type theorem for covariant representations 协变表示的世界型分解和beurling型定理
IF 0.7
Advances in Operator Theory Pub Date : 2026-08-06 DOI: 10.1007/s43036-026-00527-4
Dimple Saini, Azad Rohilla
{"title":"Wold-type decomposition and Beurling-type theorem for covariant representations","authors":"Dimple Saini,&nbsp;Azad Rohilla","doi":"10.1007/s43036-026-00527-4","DOIUrl":"10.1007/s43036-026-00527-4","url":null,"abstract":"<div><p>Using operator inequalities, we study a Wold-type decomposition of covariant representations. Building on this decomposition, we prove a Beurling-type theorem showing that every nonzero invariant subspace is uniquely determined by its wandering subspace. Our results extend classical theorems of Beurling and subsequent developments for left-invertible operators to the setting of covariant representations of <span>(C^*)</span>-correspondences, providing a unified framework for invariant subspace theory under operator inequalities.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Additive and multiplicative maps in norm on the positive cone of continuous function algebras 连续函数代数正锥上范数上的加性和乘性映射
IF 0.7
Advances in Operator Theory Pub Date : 2026-07-30 DOI: 10.1007/s43036-026-00521-w
Takeshi Miura, Natsumi Shibata
{"title":"Additive and multiplicative maps in norm on the positive cone of continuous function algebras","authors":"Takeshi Miura,&nbsp;Natsumi Shibata","doi":"10.1007/s43036-026-00521-w","DOIUrl":"10.1007/s43036-026-00521-w","url":null,"abstract":"<div><p>Let <i>X</i> and <i>Y</i> be locally compact Hausdorff spaces. We denote by <span>(C_0^+(X))</span> the cone of all non-negative real-valued continuous functions on <i>X</i> vanishing at infinity. In this paper, we consider a bijection <span>(T:C_0^+(X) rightarrow C_0^+(Y))</span> satisfying the following two norm conditions for all <span>(f, g in C_0^+(X))</span>: </p><div><div><span>$$ Vert T(f+g) Vert = Vert T(f)+T(g) Vert ,qquad Vert T(f cdot g) Vert = Vert T(f) cdot T(g) Vert . $$</span></div></div><p>The main result of this paper is that such a map <i>T</i> is a composition operator of the form <span>(T(f) = f circ tau )</span>, induced by a homeomorphism <span>(tau :Y rightarrow X)</span>. As a direct consequence of our main theorem, we obtain a positive cone version of the Gelfand–Kolmogoroff theorem.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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