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Advances in Operator Theory最新文献

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Markov invariant dynamics and Cuntz–Krieger corner algebras 马尔可夫不变动力学与Cuntz-Krieger角代数
IF 0.7
Advances in Operator Theory Pub Date : 2026-01-15 DOI: 10.1007/s43036-025-00492-4
C. Correia Ramos, Nuno Martins, Paulo R. Pinto
{"title":"Markov invariant dynamics and Cuntz–Krieger corner algebras","authors":"C. Correia Ramos,&nbsp;Nuno Martins,&nbsp;Paulo R. Pinto","doi":"10.1007/s43036-025-00492-4","DOIUrl":"10.1007/s43036-025-00492-4","url":null,"abstract":"<div><p>We consider a class of Markov interval maps <span>(fin mathcal {M}(I))</span> with <i>I</i> an interval, whose associated transition matrix <span>(A_f)</span> is necessarily primitive. Then we search for subdynamics, i.e., a subset <span>(Jsubset I)</span> and <span>(g=fvert _{J} in mathcal { M}([J]))</span>, with [<i>J</i>] the minimal closed interval containing <i>J</i>. The transition matrix <span>(A_g)</span> of <i>g</i> is obtained through successive state splittings of <span>(A_f)</span>, followed by the removal of appropriate row(s) and column(s). We prove the existence of such <i>J</i> ensuring <span>(gin mathcal {M}([J]))</span>. We also consider the Cuntz–Krieger algebra <span>(mathcal {O}_{A_{f}})</span> representation <span>(pi _{f,x})</span> on the Hilbert space associated to the <i>f</i>-orbit of each point <span>(xin J)</span>. We similarly obtain a representation <span>(pi _{g,x})</span> of <span>(mathcal {O}_{A_{g}})</span>. We prove that <span>(pi _{g,x}(mathcal {O}_{A_{g}}))</span> is a subalgebra of <span>(pi _{f,x}(mathcal {O}_{A_{f}}))</span>. By exploring this further, we show that in fact <span>(mathcal {O}_{A_{g}})</span> is a corner algebra of <span>(mathcal {O}_{A_{f}})</span> by finding a projection <span>(p_J)</span> such that <span>(mathcal {O}_{A_{g}}=p_{J},mathcal {O}_{A_{f}}p_{J})</span>. We explicitly enumerate such corner algebras for each splitting state. This method provides a systematic way to construct concrete examples of specific Cuntz–Krieger corner algebras.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145983262","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
Real interpolation methods based on metrically abundant Banach couples 基于度量丰度Banach对的实数插值方法
IF 0.7
Advances in Operator Theory Pub Date : 2026-01-12 DOI: 10.1007/s43036-025-00490-6
Per G. Nilsson
{"title":"Real interpolation methods based on metrically abundant Banach couples","authors":"Per G. Nilsson","doi":"10.1007/s43036-025-00490-6","DOIUrl":"10.1007/s43036-025-00490-6","url":null,"abstract":"<div><p>A unified approach to construct collections of K-spaces based on paramater couples with certain strong properties is formulated. This approach includes in particular the collections of K-spaces and small k-spaces.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145982845","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 properties and essential spectra of bounded operators on semi-Hilbertian spaces 半hilbertian空间上有界算子的Fredholm性质和本质谱
IF 0.7
Advances in Operator Theory Pub Date : 2025-12-18 DOI: 10.1007/s43036-025-00486-2
Ruiyao Xue, Guolin Hou
{"title":"Fredholm properties and essential spectra of bounded operators on semi-Hilbertian spaces","authors":"Ruiyao Xue,&nbsp;Guolin Hou","doi":"10.1007/s43036-025-00486-2","DOIUrl":"10.1007/s43036-025-00486-2","url":null,"abstract":"<div><p>Given a bounded positive linear operator <i>A</i> on a Hilbert space <span>(mathcal {X})</span>, this operator induces a semi-Hilbertian structure on <span>(mathcal {X})</span>. For a bounded linear operator <i>T</i> defined on the corresponding semi-Hilbertian space, we introduce a new definition of a Fredholm operator that is compatible with the semi-Hilbertian structure. Based on this definition, we proceed to define the essential spectra of <i>T</i> and establish their fundamental properties. Within this framework, we consider the bounded off-diagonal operator matrix <span>(mathbb {T} = begin{pmatrix} 0 &amp; M N &amp; 0 end{pmatrix})</span> acting on the semi-Hilbertian space and demonstrate that the essential spectra of <span>(mathbb {T})</span> are entirely determined by the essential spectra of the products <i>MN</i> and <i>NM</i>. Finally, an illustrative example is provided to substantiate the theoretical conclusions.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145778718","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
Some properties of the finitely additive vector integral 有限加性向量积分的一些性质
IF 0.7
Advances in Operator Theory Pub Date : 2025-12-10 DOI: 10.1007/s43036-025-00489-z
Gianluca Cassese
{"title":"Some properties of the finitely additive vector integral","authors":"Gianluca Cassese","doi":"10.1007/s43036-025-00489-z","DOIUrl":"10.1007/s43036-025-00489-z","url":null,"abstract":"<div><p>We prove some results concerning the finitely additive, vector integrals of Bochner and Pettis and their representation over a countably additive probability space. An application to the non compact Choquet theorem is also provided.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00489-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145729639","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
Minimality and effectiveness of the groupoid associated to a self-similar ultragraph 与自相似超图相关的类群的极小性和有效性
IF 0.7
Advances in Operator Theory Pub Date : 2025-12-09 DOI: 10.1007/s43036-025-00487-1
Hossein Larki, Najmeh Rajabzadeh-Hasiri
{"title":"Minimality and effectiveness of the groupoid associated to a self-similar ultragraph","authors":"Hossein Larki,&nbsp;Najmeh Rajabzadeh-Hasiri","doi":"10.1007/s43036-025-00487-1","DOIUrl":"10.1007/s43036-025-00487-1","url":null,"abstract":"<div><p>The notion of a self-similar ultragraph <span>((G,mathcal {U},varphi ))</span> and its <span>(C^*)</span>-algebra <span>(mathcal {O}_{G,mathcal {U}})</span> were introduced in our recent work, where we proposed inverse semigroup and groupoid models for such <span>(C^*)</span>-algebras as well. In this paper, we investigate minimality and effectiveness of the groupoid of a self-similar ultragraph <span>((G,mathcal {U},varphi ))</span>. In particular, we obtain a result for simplicity of the <span>(C^*)</span>-algebras <span>(mathcal {O}_{G,mathcal {U}})</span> in a certain case.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145729593","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
Weyl type theorems for hypercyclic, supercyclic, and Toeplitz operators 超循环、超循环和Toeplitz算子的Weyl型定理
IF 0.7
Advances in Operator Theory Pub Date : 2025-11-27 DOI: 10.1007/s43036-025-00488-0
Simi Thomas, Thankarajan Prasad, Shery Fernandez
{"title":"Weyl type theorems for hypercyclic, supercyclic, and Toeplitz operators","authors":"Simi Thomas,&nbsp;Thankarajan Prasad,&nbsp;Shery Fernandez","doi":"10.1007/s43036-025-00488-0","DOIUrl":"10.1007/s43036-025-00488-0","url":null,"abstract":"<div><p>In this paper, we study property <span>((UW_E))</span> for hypercyclic and supercyclic operators. The stability of variants of Weyl type theorems under compact perturbations for Toeplitz operators on the Bergman space is also studied. We also provide some examples of Toeplitz operators satisfying Weyl type theorems on the Bergman space and the harmonic Bergman space.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145612865","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
Analytic Hardy space and Cauchy transform on Sierpinski triangle 解析Hardy空间与Sierpinski三角形上的Cauchy变换
IF 0.7
Advances in Operator Theory Pub Date : 2025-11-14 DOI: 10.1007/s43036-025-00485-3
Yi Xu, Hongdou Qu, Yin Cai
{"title":"Analytic Hardy space and Cauchy transform on Sierpinski triangle","authors":"Yi Xu,&nbsp;Hongdou Qu,&nbsp;Yin Cai","doi":"10.1007/s43036-025-00485-3","DOIUrl":"10.1007/s43036-025-00485-3","url":null,"abstract":"<div><p>In this paper, we consider analytic Hardy spaces associated with fractal domains in the complex plane. In 2013, Dong et al. obtained a positive solution to the Cantor set conjecture in (Adv Math 232:543–570, 2013) for the Cauchy transforms on the Sierpinski triangle. In this paper, we achieve a deeper understanding of these Cauchy transforms by showing that they do not belong to any Hardy space on <span>(triangle ^*,)</span> where <span>(triangle ^*= widehat{{mathbb {C}}}setminus triangle )</span> and <span>(triangle )</span> is the compact regular triangle with vertexes <span>({varepsilon _k=e^{2kpi i/3}, k=0,1,2}.)</span> Along the way, a Hardy–Littlewood-type theorem for general domains, which is of independent interests, is established.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145510567","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
Existence and multiplicity of normalized solutions for p-Laplacian Schrödinger–Poisson equations with Hardy term Hardy项p- laplace Schrödinger-Poisson方程归一化解的存在性和多重性
IF 0.7
Advances in Operator Theory Pub Date : 2025-11-08 DOI: 10.1007/s43036-025-00478-2
Mingxue Li, Jiafeng Zhang
{"title":"Existence and multiplicity of normalized solutions for p-Laplacian Schrödinger–Poisson equations with Hardy term","authors":"Mingxue Li,&nbsp;Jiafeng Zhang","doi":"10.1007/s43036-025-00478-2","DOIUrl":"10.1007/s43036-025-00478-2","url":null,"abstract":"<div><p>This paper considers the existence and multiplicity of normalized solutions for the following Schrödinger–Poisson equation involving <i>p</i>-Laplacian operator and Hardy term </p><div><div><span>$$begin{aligned} {left{ begin{array}{ll}-Delta _p u-frac{mu }{|x|^p}|u|^{p-2} u+kappa phi |u|^{p-2} u=lambda |u|^{p-2} u+|u|^{q-2} u, &amp; text { in } mathbb {R}^3, -Delta phi =|u|^p, &amp; text { in } mathbb {R}^3, int _{mathbb {R}^3}|u|^p =c&gt;0, end{array}right. } end{aligned}$$</span></div></div><p>where <span>(1&lt;p&lt;3)</span>, <span>(p+frac{p^{2}}{3}&lt;q&lt;p^{*}:=frac{3p}{3-p})</span>, <span>(0le mu &lt;bar{mu }:=left( frac{3-p}{p}right) ^p)</span>, <span>(lambda )</span> is a Lagrange multiplier and <span>(kappa &gt;0)</span> is a parameter. We prove the existence of normalized solution by using the Pohozaev manifold and obtain the infinitely many radial solutions by a fountain theorem type argument. Moreover, we explore the asymptotic behavior of normalized solutions as <span>(mu rightarrow 0)</span> and <span>(kappa rightarrow 0)</span>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145510465","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
Reversible topological semigroups of uniformly asymptotically regular mappings on locally convex spaces 局部凸空间上一致渐近正则映射的可逆拓扑半群
IF 0.7
Advances in Operator Theory Pub Date : 2025-11-07 DOI: 10.1007/s43036-025-00483-5
Khadime Salame
{"title":"Reversible topological semigroups of uniformly asymptotically regular mappings on locally convex spaces","authors":"Khadime Salame","doi":"10.1007/s43036-025-00483-5","DOIUrl":"10.1007/s43036-025-00483-5","url":null,"abstract":"<div><p>This paper is concerned with the extension to semigroups two interesting results by Vijayaraju that guarantee the existence of a fixed point for asumptotically nonexpansive and uniformly asymptotically regular mappings on a star-shaped set in a separated locally convex space. We prove that those results are extensible to the class of (left) reversible topological semigroups <i>S</i> and can be improved significantly by dropping some conditions, and study some related results in connection with amenability of AP(<i>S</i>) and WAP(<i>S</i>).</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145456291","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
Hilbert numbers of Sobolev spaces with mixed smoothness in the sup-norm 上范数中混合光滑Sobolev空间的Hilbert数
IF 0.7
Advances in Operator Theory Pub Date : 2025-11-06 DOI: 10.1007/s43036-025-00475-5
Van Kien Nguyen
{"title":"Hilbert numbers of Sobolev spaces with mixed smoothness in the sup-norm","authors":"Van Kien Nguyen","doi":"10.1007/s43036-025-00475-5","DOIUrl":"10.1007/s43036-025-00475-5","url":null,"abstract":"<div><p>In this paper, we study Hilbert numbers of embedding of Sobolev space of mixed smoothness <span>(H^{s,r}_{textrm{mix}}({{mathbb {T}}}^d))</span> on the torus <span>({{mathbb {T}}}^d)</span> into <span>(L_infty ({{mathbb {T}}}^d))</span> and the Wiener class <span>(mathcal {A}({{mathbb {T}}}^d))</span>. We obtain the exact asymptotic order of Hilbert numbers of these embeddings and the asymptotic constant for the embedding into <span>(mathcal {A}({{mathbb {T}}}^d))</span>. We also obtain the asymptotic constant of Hilbert numbers of embedding of Gaussian weighted Sobobev space <span>(H^s({{mathbb {R}}}^d,gamma ))</span> into <span>(mathcal {A}({{mathbb {R}}}^d,gamma ))</span> which is a counterpart of the Wiener class <span>(mathcal {A}({{mathbb {T}}}^d))</span>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145456423","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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