Advances in Operator Theory最新文献

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Weak characterizations of the Schur property 舒尔性质的弱表征
IF 0.7
Advances in Operator Theory Pub Date : 2025-06-05 DOI: 10.1007/s43036-025-00451-z
W. M. Ruess, C. P. Stegall
{"title":"Weak characterizations of the Schur property","authors":"W. M. Ruess,&nbsp;C. P. Stegall","doi":"10.1007/s43036-025-00451-z","DOIUrl":"10.1007/s43036-025-00451-z","url":null,"abstract":"<div><p>Recent results on weak characterizations of the Schur property for Banach spaces, based on techniques of bimonotone bases in Banach spaces, are extended to Fréchet—and more general locally convex—spaces by short-cut proofs based on arguments of topological nature.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00451-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162588","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
Matrix systems, algebras, and open maps 矩阵系统,代数和开映射
IF 0.7
Advances in Operator Theory Pub Date : 2025-06-01 DOI: 10.1007/s43036-025-00448-8
Stephan Weis
{"title":"Matrix systems, algebras, and open maps","authors":"Stephan Weis","doi":"10.1007/s43036-025-00448-8","DOIUrl":"10.1007/s43036-025-00448-8","url":null,"abstract":"<div><p>Every state on the algebra <span>(textrm{M}_n)</span> of complex <span>(ntimes n)</span> matrices restricts to a state on any matrix system. Whereas the restriction to a matrix system is generally not open, we prove that the restriction to every *-subalgebra of <span>(textrm{M}_n)</span> is open. This simplifies topology problems in matrix theory and quantum information theory.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00448-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145160849","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
Generalised Morrey sequence spaces 广义Morrey序列空间
IF 0.7
Advances in Operator Theory Pub Date : 2025-05-31 DOI: 10.1007/s43036-025-00443-z
Dorothee D. Haroske, Leszek Skrzypczak
{"title":"Generalised Morrey sequence spaces","authors":"Dorothee D. Haroske,&nbsp;Leszek Skrzypczak","doi":"10.1007/s43036-025-00443-z","DOIUrl":"10.1007/s43036-025-00443-z","url":null,"abstract":"<div><p>Generalised Morrey (function) spaces enjoyed some interest recently and found applications to PDE. Here we turn our attention to their discrete counterparts. We define generalised Morrey sequence spaces <span>(m_{varphi ,p}=m_{varphi ,p}({mathbb {Z}}^d))</span>. They are natural generalisations of the classical Morrey sequence spaces <span>(m_{u,p})</span>, <span>(0&lt;ple u&lt;infty )</span>, which were studied earlier. We consider some basic features of the spaces as well as embedding properties such as continuity, compactness and strict singularity.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00443-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171883","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
On (L_{exp }) and (L log L) Zygmund’s spaces and its r-convexifications: the Orlicz–Luxemburg point of view 论(L_{exp })和(L log L) Zygmund的空间及其r-凸化:Orlicz-Luxemburg的观点
IF 0.7
Advances in Operator Theory Pub Date : 2025-05-28 DOI: 10.1007/s43036-025-00450-0
Fernando Mayoral
{"title":"On (L_{exp }) and (L log L) Zygmund’s spaces and its r-convexifications: the Orlicz–Luxemburg point of view","authors":"Fernando Mayoral","doi":"10.1007/s43036-025-00450-0","DOIUrl":"10.1007/s43036-025-00450-0","url":null,"abstract":"<div><p>The present paper is devoted to obtain numerical estimations for the equivalences between the Hardy–Littlewood norms of Zygmund’s spaces, <span>(L_{exp })</span> and <span>(Llog L,)</span> and the Luxemburg norms associated to concrete Young functions that define these spaces. Moreover, for a (finite) measure we compute the equivalence constants between the Hardy–Littlewood norms of Zygmund’s spaces and the norms as associate (Köthe-dual) spaces. It is also proved that, for each <span>(0&lt;r&lt;1,)</span> the quasinorm of the <i>r</i>-convexification <span>(L^r_{exp },)</span> of <span>(L_{exp },)</span> is equivalent to a norm. In the opposite, the quasinorm of the <i>r</i>-convexification <span>(L^rlog L,)</span> of <span>(Llog L,)</span> is not equivalent to a norm. In the atomic case, the <i>r</i>-convexification <span>(L^rlog L)</span> has a separating dual. We analyse the weak compactness of the multiplication operators from <span>(L^{infty })</span> to <span>(L_{exp })</span> and from <span>(Llog L)</span> to <span>(L^1.)</span> From the weak compactness of the embeddings follows the reflexivity of certain Lions–Peetre interpolated spaces.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00450-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171425","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
Interpolation of the inner measure of bilinear operators by the real method 用实数法插值双线性算子的内测度
IF 0.7
Advances in Operator Theory Pub Date : 2025-05-27 DOI: 10.1007/s43036-025-00444-y
Fernando Cobos, Luz M. Fernández-Cabrera, Antón Martínez
{"title":"Interpolation of the inner measure of bilinear operators by the real method","authors":"Fernando Cobos,&nbsp;Luz M. Fernández-Cabrera,&nbsp;Antón Martínez","doi":"10.1007/s43036-025-00444-y","DOIUrl":"10.1007/s43036-025-00444-y","url":null,"abstract":"<div><p>We describe a procedure for extending the inner measure <span>(beta _{_{mathcal {I}}})</span> associated to an operator ideal <span>(mathcal {I})</span> to a measure <span>(beta _{_{mathfrak {J}}})</span> for bounded bilinear operators <i>T</i>. When <span>(mathcal {I})</span> is injective and closed, we show that <span>(beta _{_{mathfrak {J}}}(T)=0)</span> if and only if <span>(T=RS)</span> for some bounded bilinear operator <i>S</i> and <span>(Rin mathcal {I})</span>. If <span>(mathcal {I})</span> satisfies the <span>(Sigma _r)</span>-condition, then we establish a convexity inequality for the measure <span>(beta _{_{mathfrak {J}}})</span> of a bilinear operator interpolated by the real method.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00444-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170565","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
Structure and applications of n-quasi exponentially m-isometric operators n-拟指数m-等距算子的结构与应用
IF 0.8
Advances in Operator Theory Pub Date : 2025-05-26 DOI: 10.1007/s43036-025-00445-x
Abeer A. Al Dohiman, Mohamed Amine Aouichaoui, Sid Ahmed Ould Ahmed Mahmoud
{"title":"Structure and applications of n-quasi exponentially m-isometric operators","authors":"Abeer A. Al Dohiman,&nbsp;Mohamed Amine Aouichaoui,&nbsp;Sid Ahmed Ould Ahmed Mahmoud","doi":"10.1007/s43036-025-00445-x","DOIUrl":"10.1007/s43036-025-00445-x","url":null,"abstract":"<div><p>In this paper, we aim to extend the established theory of exponentially <i>m</i>-isometric operators by introducing and exploring the concept of <i>n</i>-quasi-exponentially m-isometric operators. This generalization allows us to investigate a broader class of operators. We provide a comprehensive analysis of various key properties of these operators, which are illustrated through specific matrix representations. An examination of their spectral properties is also provided. The open questions presented at the end pave the way for further research and the continued advancement of the theory of <i>m</i>-isometries and related operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144140233","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
Extension of m-isometric weighted composition operators on directed graphs 有向图上m等距加权复合算子的推广
IF 0.8
Advances in Operator Theory Pub Date : 2025-05-23 DOI: 10.1007/s43036-025-00447-9
V. Devadas, E. Shine Lal, T. Prasad
{"title":"Extension of m-isometric weighted composition operators on directed graphs","authors":"V. Devadas,&nbsp;E. Shine Lal,&nbsp;T. Prasad","doi":"10.1007/s43036-025-00447-9","DOIUrl":"10.1007/s43036-025-00447-9","url":null,"abstract":"<div><p>In this paper, we discuss <i>k</i>-quasi-<i>m</i>-isometric composition operators and weighted composition operators on directed graphs with one circuit and more than one branching vertex.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144117625","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
Regular traces on ideals in (mathcal {L}(H)) 规律的痕迹就在理想之中 (mathcal {L}(H))
IF 0.8
Advances in Operator Theory Pub Date : 2025-05-16 DOI: 10.1007/s43036-025-00446-w
F. Sukochev, D. Zanin
{"title":"Regular traces on ideals in (mathcal {L}(H))","authors":"F. Sukochev,&nbsp;D. Zanin","doi":"10.1007/s43036-025-00446-w","DOIUrl":"10.1007/s43036-025-00446-w","url":null,"abstract":"<div><p>On a Banach ideal the set of continuous traces is spanned by the set of positive traces. We extend this result by showing that on an arbitrary ideal the set of all regular traces is the linear span of the set of positive traces.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144073621","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
Power-regularity of weighted shift operators
IF 0.8
Advances in Operator Theory Pub Date : 2025-05-13 DOI: 10.1007/s43036-025-00442-0
Chaolong Hu, Youqing Ji
{"title":"Power-regularity of weighted shift operators","authors":"Chaolong Hu,&nbsp;Youqing Ji","doi":"10.1007/s43036-025-00442-0","DOIUrl":"10.1007/s43036-025-00442-0","url":null,"abstract":"<div><p>A linear bounded operator <i>T</i> on a complex Banach space <i>X</i> is said to be <i>power-regular</i> if the sequence <span>({Vert T^n xVert ^{frac{1}{n}}}_{n=1}^{infty })</span> is convergent for every <span>(xin X)</span>. For unilateral weighted shift <i>S</i>, we give a sufficient condition that <i>S</i> is power-regular. As an application, we construct a class of power-regular operators. Moreover, we show that there exist invertible power-regular bilateral weighted shifts, whose inverses are not power-regular.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143944180","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
Spectral decomposition of power-bounded operators: the finite spectrum case 幂有界算子的谱分解:有限谱情况
IF 0.8
Advances in Operator Theory Pub Date : 2025-05-12 DOI: 10.1007/s43036-025-00441-1
Shiho Oi, Jyamira Oppekepenguin
{"title":"Spectral decomposition of power-bounded operators: the finite spectrum case","authors":"Shiho Oi,&nbsp;Jyamira Oppekepenguin","doi":"10.1007/s43036-025-00441-1","DOIUrl":"10.1007/s43036-025-00441-1","url":null,"abstract":"<div><p>In this paper, we investigate power-bounded operators, including surjective isometries, on Banach spaces. Koehler and Rosenthal asserted that an isolated point in the spectrum of a surjective isometry on a Banach space lies in the point spectrum, with the corresponding eigenspace having an invariant complement. However, they did not provide a detailed proof of this claim, at least as understood by the authors of this manuscript. Here, by applications of a theorem of Gelfand and the Riesz projections, we demonstrate that the theorem of Koehler and Rosenthal holds for any power-bounded operator on a Banach space. This not only furnishes a detailed proof of the theorem but also slightly generalizes its scope. As a result, we establish that if <span>(T: X rightarrow X)</span> is a power-bounded operator on a Banach space <i>X</i> whose spectrum consists of finitely many points <span>({lambda _1, lambda _2, dots , lambda _m})</span>, then for every <span>(1 le i, j le m)</span>, there exist projections <span>(P_j)</span> on <i>X</i> such that <span>(P_iP_j=delta _{ij}P_i)</span>, <span>(sum _{j=1}^mP_j=I)</span>, and <span>(T=Sigma _{j=1}^m lambda _j P_j)</span>. It follows that such an operator <i>T</i> is an algebraic operator.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143938524","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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