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Advances in Operator Theory最新文献

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Mean Ergodic type theorems by means of ideal convergence 用理想收敛方法研究平均遍历型定理
IF 0.7
Advances in Operator Theory Pub Date : 2025-07-06 DOI: 10.1007/s43036-025-00462-w
Gencay Oğuz, Mustafa Gülfırat
{"title":"Mean Ergodic type theorems by means of ideal convergence","authors":"Gencay Oğuz,&nbsp;Mustafa Gülfırat","doi":"10.1007/s43036-025-00462-w","DOIUrl":"10.1007/s43036-025-00462-w","url":null,"abstract":"<div><p>Let <i>X</i> be a Banach space and <i>T</i> be a bounded linear operator on <i>X</i>. Ergodic type theorems investigate the strong convergence of the Cesàro averages given by <span>(M_n(T):=dfrac{1}{n}sum nolimits _{k=1}^{n}T^k)</span>. The main aim of this paper is to give an analogue of mean ergodic type theorems by replacing the ordinary convergence with the ideal convergence. We also present an important inequality that immediately leads to a characterization for the set of closure of the range of <span>(I-T)</span>. The results presented in this paper extend some existing theorems in the literature.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162279","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 structure of ({mathcal {U}}_n)-twisted power partial isometries ({mathcal {U}}_n) -扭转幂部分等距的结构
IF 0.7
Advances in Operator Theory Pub Date : 2025-07-04 DOI: 10.1007/s43036-025-00460-y
Athul Augustine, P. Shankar
{"title":"The structure of ({mathcal {U}}_n)-twisted power partial isometries","authors":"Athul Augustine,&nbsp;P. Shankar","doi":"10.1007/s43036-025-00460-y","DOIUrl":"10.1007/s43036-025-00460-y","url":null,"abstract":"<div><p>Let <span>(n&gt;1)</span> and let <span>({U_{ij}}_{1le i&lt;jle n})</span> be <span>(natopwithdelims ()2)</span> commuting unitaries on a Hilbert space <span>({mathcal {H}})</span>. Suppose <span>(U_{ji}:=U^*_{ij})</span>, <span>(1le i&lt;jle n)</span>. An <i>n</i>-tuple of power partial isometries <span>((V_1,...,V_n))</span> on Hilbert space <span>({mathcal {H}})</span> is called <span>({mathcal {U}}_n)</span>-twisted power partial isometry with respect to <span>({U_{ij}}_{i&lt;j})</span> (or simply <span>({mathcal {U}}_n)</span>-twisted power partial isometry if <span>({U_{ij}}_{i&lt;j})</span> is clear from the context) if <span>(V_i^*V_j=U_{ij}V_jV^*_i, ~~ V_iV_j=U_{ji}V_jV_i ~~text {and}~~ V_kU_{ij}=U_{ij}V_k~~(i,j,k=1,2,...,n,~text {and}~ine j).)</span> We prove that each <span>({mathcal {U}}_n)</span>-twisted power partial isometry admits a Halmos and Wallen (J Math Mech 19:657–663, 1969/1970) type orthogonal decomposition. We provide a concrete model for the decomposition of <span>({mathcal {U}}_n)</span>-twisted power partial isometries.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161925","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
Invariant submodules of modular operators and Lomonosov type theorem for Hilbert C*-modules 模算子的不变子模及Hilbert C*模的Lomonosov型定理
IF 0.7
Advances in Operator Theory Pub Date : 2025-07-03 DOI: 10.1007/s43036-025-00461-x
Kamran Sharifi
{"title":"Invariant submodules of modular operators and Lomonosov type theorem for Hilbert C*-modules","authors":"Kamran Sharifi","doi":"10.1007/s43036-025-00461-x","DOIUrl":"10.1007/s43036-025-00461-x","url":null,"abstract":"<div><p>In this paper, we study basic properties of compact operators on Hilbert C*-modules over an arbitrary finite dimensional C*-algebra <span>(mathcal {A})</span>. We introduce the notions of invariant and hyperinvariant submodules in the setting of Hilbert C*-modules and prove a Lomonosov type theorem for compact modular operators on such modules. Specifically, we show that every nonzero compact modular operator acting on a Hilbert <span>(mathcal {A})</span>-module admits a proper nonzero hyperinvariant submodule.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161700","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 Shilov boundary for a local operator system 局部算子系统的希洛夫边界
IF 0.7
Advances in Operator Theory Pub Date : 2025-07-02 DOI: 10.1007/s43036-025-00459-5
Maria Joiţa
{"title":"The Shilov boundary for a local operator system","authors":"Maria Joiţa","doi":"10.1007/s43036-025-00459-5","DOIUrl":"10.1007/s43036-025-00459-5","url":null,"abstract":"<div><p>In this paper, we introduce the notion of Shilov boundary ideal for a local operator system and investigate some of its properties.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160882","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
A summability principle and applications 可求和性原理及其应用
IF 0.7
Advances in Operator Theory Pub Date : 2025-06-28 DOI: 10.1007/s43036-025-00458-6
N. G. Albuquerque, G. Araújo, L. Rezende, J. Santos
{"title":"A summability principle and applications","authors":"N. G. Albuquerque,&nbsp;G. Araújo,&nbsp;L. Rezende,&nbsp;J. Santos","doi":"10.1007/s43036-025-00458-6","DOIUrl":"10.1007/s43036-025-00458-6","url":null,"abstract":"<div><p>This paper investigates summability principles for multilinear summing operators. The main result presents a novel inclusion theorem for a class of summing operators, which generalizes several classical results. As applications, we derive improved estimates for Hardy–Littlewood inequalities on multilinear forms and prove a Grothendieck-type coincidence result in anisotropic settings.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170066","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
A characterization of compact operators on (ell ^p)-spaces (ell ^p) -空间上紧算子的刻画
IF 0.7
Advances in Operator Theory Pub Date : 2025-06-25 DOI: 10.1007/s43036-025-00455-9
Mortaza Abtahi
{"title":"A characterization of compact operators on (ell ^p)-spaces","authors":"Mortaza Abtahi","doi":"10.1007/s43036-025-00455-9","DOIUrl":"10.1007/s43036-025-00455-9","url":null,"abstract":"<div><p>Let <i>A</i> be a Banach space, <span>(p&gt;1,)</span> and <span>(1/p+1/q=1.)</span> If a sequence <span>(textbf{a}=(a_i))</span> in <i>A</i> has a finite <i>p</i>-sum, then the operator <span>(Lambda _textbf{a}:ell ^qrightarrow A,)</span> defined by <span>(Lambda _textbf{a}(beta )=sum _{i=1}^infty beta _i a_i,)</span> <span>(beta =(beta _i)in ell ^q,)</span> is compact. We present a characterization of compact operators <span>(Lambda :ell ^qrightarrow A,)</span> and prove that <span>(Lambda )</span> is compact if and only if <span>(Lambda =Lambda _textbf{a},)</span> for some sequence <span>(textbf{a}=(a_i))</span> in <i>A</i> with <span>(left{ left( phi (a_i) right) : phi in A^*, Vert phi Vert leqslant 1 right} )</span> being a totally bounded set in <span>(ell ^p.)</span> For a sequence <span>((T_i))</span> of bounded operators on a Hilbert space <span>(mathcal {H},)</span> the corresponding operator <span>({{varvec{T}}}:ell ^qrightarrow mathbb {B}(mathcal {H}),)</span> defined by <span>({{varvec{T}}}(beta ) = sum _{i=1}^infty beta _i T_i,)</span> is compact if and only if the set <span>({langle {{varvec{T}}}x,x rangle :Vert xVert =1})</span> is a totally bounded subset of <span>(ell ^p,)</span> where <span>(langle {{varvec{T}}}x,x rangle = (langle T_1 x,x rangle , langle T_2 x,x rangle , dotsc ),)</span> for <span>(xin mathcal {H}.)</span> Similar results are established for <span>(p=1)</span> and <span>(p=infty .)</span></p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169726","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
Correction: Ideals of mid p-summing operators: a tensor product approach 修正：中间p求和算子的理想：张量积方法
IF 0.7
Advances in Operator Theory Pub Date : 2025-06-19 DOI: 10.1007/s43036-025-00457-7
Aleena Philip, Deepika Baweja
{"title":"Correction: Ideals of mid p-summing operators: a tensor product approach","authors":"Aleena Philip,&nbsp;Deepika Baweja","doi":"10.1007/s43036-025-00457-7","DOIUrl":"10.1007/s43036-025-00457-7","url":null,"abstract":"","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145167416","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
On (hbox {w}^*)-Dunford–Pettis operators 在(hbox {w}^*) -邓福德-佩蒂斯运营商
IF 0.7
Advances in Operator Theory Pub Date : 2025-06-11 DOI: 10.1007/s43036-025-00454-w
Şafak Alpay, Svetlana Gorokhova
{"title":"On (hbox {w}^*)-Dunford–Pettis operators","authors":"Şafak Alpay,&nbsp;Svetlana Gorokhova","doi":"10.1007/s43036-025-00454-w","DOIUrl":"10.1007/s43036-025-00454-w","url":null,"abstract":"<div><p>A subclass of weak Dunford–Pettis operators named <span>(hbox {w}^*)</span>DP operators is under investigation. The article studies conditions under which <span>(hbox {w}^*)</span>DP-operators have properties such as (weak) compactness and limitedness, and the relationship of <span>(hbox {w}^*)</span>DP operators with Dunford–Pettis operators. Several further topics related to these operators are investigated.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-06-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163814","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
Lip-linear operators and their connection to Lipschitz tensor products 唇线性算子及其与李普希茨张量积的联系
IF 0.7
Advances in Operator Theory Pub Date : 2025-06-10 DOI: 10.1007/s43036-025-00453-x
Athmane Ferradi, Khalil Saadi
{"title":"Lip-linear operators and their connection to Lipschitz tensor products","authors":"Athmane Ferradi,&nbsp;Khalil Saadi","doi":"10.1007/s43036-025-00453-x","DOIUrl":"10.1007/s43036-025-00453-x","url":null,"abstract":"<div><p>The linear operators defined on the Lipschitz projective tensor product <span>(X {widehat{boxtimes }}_{pi }E)</span> motivate the study of a distinct class of operators acting on the cartesian product <span>(Xtimes E)</span>. These operators, called Lip-linear operators, form a Banach space denoted by <span>(LipL_{0}left( Xtimes E;Fright) .)</span> This space provides an intermediate setting between bilinear operators and two-Lipschitz operators. We establish a natural identification between <span>(LipL_{0}left( Xtimes E;Fright) )</span> and <span>({mathcal {L}} (X{widehat{boxtimes }}_{pi }E;F) ,)</span> which also relates it to the space of bilinear operators <span>({mathcal {B}}left( {mathcal {F}}(X)times E;Fright) )</span>. Furthermore, we extend summability concepts within this category, with a particular focus on integral and dominated (<i>p</i>; <i>q</i>)-summing operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163671","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
On Roth-type solvability criteria for generalized Sylvester matrix and operator equations 广义Sylvester矩阵和算子方程的roth型可解准则
IF 0.7
Advances in Operator Theory Pub Date : 2025-06-09 DOI: 10.1007/s43036-025-00452-y
Hua Wang, Xiaoju Jin, Junjie Huang
{"title":"On Roth-type solvability criteria for generalized Sylvester matrix and operator equations","authors":"Hua Wang,&nbsp;Xiaoju Jin,&nbsp;Junjie Huang","doi":"10.1007/s43036-025-00452-y","DOIUrl":"10.1007/s43036-025-00452-y","url":null,"abstract":"<div><p>In this paper, Roth-type solvability criteria are proposed for the generalized Sylvester equation <span>(AXB+CYD+EZF=G)</span> on finite dimensional spaces and infinite dimensional Hilbert spaces, respectively. Moreover, we give a solvability condition for the operator equation <span>(AXB-CXD = E)</span> by only using one invertible operator.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163506","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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