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Advances in Operator Theory最新文献

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Gleason’s problem for harmonic mixed norm spaces in bounded star-shaped domains 有界星形域调和混合范数空间的Gleason问题
IF 0.7
Advances in Operator Theory Pub Date : 2025-07-16 DOI: 10.1007/s43036-025-00467-5
Ivana Savković
{"title":"Gleason’s problem for harmonic mixed norm spaces in bounded star-shaped domains","authors":"Ivana Savković","doi":"10.1007/s43036-025-00467-5","DOIUrl":"10.1007/s43036-025-00467-5","url":null,"abstract":"<div><p>We solve Gleason’s problem for harmonic mixed norm spaces <span>(B^{p,q}_alpha (Omega ),)</span> where <span>(p,q ge 1, alpha &gt;0,)</span> on bounded star-shaped domains in <span>({mathbb {R}}^n,)</span> in a slightly more general form than the standard one, specifically for higher-order derivatives. The approach here is functional analytic, in particular, we first discuss the boundedness of certain integral operators, and then we prove that Gleason’s problem is solvable on harmonic mixed norm spaces <span>(B^{p,q}_alpha (Omega ).)</span></p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166116","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
Lorentz Herz-type Besov and Triebel-Lizorkin spaces Lorentz herz型Besov和triiebel - lizorkin空间
IF 0.7
Advances in Operator Theory Pub Date : 2025-07-13 DOI: 10.1007/s43036-025-00463-9
Douadi Drihem
{"title":"Lorentz Herz-type Besov and Triebel-Lizorkin spaces","authors":"Douadi Drihem","doi":"10.1007/s43036-025-00463-9","DOIUrl":"10.1007/s43036-025-00463-9","url":null,"abstract":"<div><p>In this paper, we introduce a new family of function spaces of Besov-Triebel-Lizorkin type. We present the <span>(varphi )</span>-transform characterization of these spaces in the sense of Frazier and Jawerth and we prove their Sobolev and Franke-Jewarth embeddings. Also, we establish the smooth atomic, molecular and wavelet decomposition of these function spaces. Characterizations by ball means of differences are given. Finally, we investigate a series of examples which play an important role in the study of function spaces of Besov-Triebel-Lizorkin type.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165278","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
Composition operators in (L^{2}(Sigma ))-semi-Hilbertian spaces (L^{2}(Sigma )) -半希尔伯特空间中的复合算子
IF 0.7
Advances in Operator Theory Pub Date : 2025-07-12 DOI: 10.1007/s43036-025-00465-7
H. Emamalipour, M. R. Jabbarzadeh, S. Mohammadpour
{"title":"Composition operators in (L^{2}(Sigma ))-semi-Hilbertian spaces","authors":"H. Emamalipour,&nbsp;M. R. Jabbarzadeh,&nbsp;S. Mohammadpour","doi":"10.1007/s43036-025-00465-7","DOIUrl":"10.1007/s43036-025-00465-7","url":null,"abstract":"<div><p>In this paper, we discuss measure-theoretic characterizations for composition operators in some operator classes on <span>(L^{2}(Sigma ))</span>-semi-Hilbertian spaces with respect to positive multiplication operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164958","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
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
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