Using the Wold–von Neumann decomposition for the isometric covariant representations due to Muhly and Solel, we prove an explicit representation of the commutant of a doubly commuting pure isometric representation of the product system over (mathbb {N}_0^{k}.) As an application we study a complete characterization of invariant subspaces for a doubly commuting pure isometric representation of the product system. This provides us a complete set of isomorphic invariants. Finally, we classify a large class of an isometric covariant representations of the product system.
{"title":"A Characterization of Invariant Subspaces for Isometric Representations of Product System over $$mathbb {N}_0^{k}$$","authors":"Dimple Saini, Harsh Trivedi, Shankar Veerabathiran","doi":"10.1007/s11785-024-01520-6","DOIUrl":"https://doi.org/10.1007/s11785-024-01520-6","url":null,"abstract":"<p>Using the Wold–von Neumann decomposition for the isometric covariant representations due to Muhly and Solel, we prove an explicit representation of the commutant of a doubly commuting pure isometric representation of the product system over <span>(mathbb {N}_0^{k}.)</span> As an application we study a complete characterization of invariant subspaces for a doubly commuting pure isometric representation of the product system. This provides us a complete set of isomorphic invariants. Finally, we classify a large class of an isometric covariant representations of the product system.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140570416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-02DOI: 10.1007/s11785-024-01518-0
Ludovick Bouthat
In a recent article, Chávez, Garcia and Hurley introduced a new family of norms (Vert cdot Vert _{{textbf {X}},d}) on the space of (n times n) complex matrices which are induced by random vectors ({textbf {X}}) having finite d-moments. Therein, the authors asked under which conditions the norms induced by a scalar multiple of ({textbf {X}}) are submultiplicative. In this paper, this question is completely answered by proving that this is always the case, as long as the entries of ({textbf {X}}) have finite p-moments for (p=max {2+varepsilon ,d}).
{"title":"On the Submultiplicativity of Matrix Norms Induced by Random Vectors","authors":"Ludovick Bouthat","doi":"10.1007/s11785-024-01518-0","DOIUrl":"https://doi.org/10.1007/s11785-024-01518-0","url":null,"abstract":"<p>In a recent article, Chávez, Garcia and Hurley introduced a new family of norms <span>(Vert cdot Vert _{{textbf {X}},d})</span> on the space of <span>(n times n)</span> complex matrices which are induced by random vectors <span>({textbf {X}})</span> having finite <i>d</i>-moments. Therein, the authors asked under which conditions the norms induced by a scalar multiple of <span>({textbf {X}})</span> are submultiplicative. In this paper, this question is completely answered by proving that this is always the case, as long as the entries of <span>({textbf {X}})</span> have finite <i>p</i>-moments for <span>(p=max {2+varepsilon ,d})</span>.</p>","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140570722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-01DOI: 10.1007/s11785-024-01513-5
Torsten Schröder-Zeiske, B. Fritzsche, B. Kirstein, C. Mädler
{"title":"A Potapov-Type Approach to a Particular Truncated Stieltjes Moment Problem in the Case of an Odd Number of Prescribed Matricial Moments","authors":"Torsten Schröder-Zeiske, B. Fritzsche, B. Kirstein, C. Mädler","doi":"10.1007/s11785-024-01513-5","DOIUrl":"https://doi.org/10.1007/s11785-024-01513-5","url":null,"abstract":"","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140352652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-04-01DOI: 10.1007/s11785-024-01510-8
N. Braha, Toufik Mansour, M. Mursaleen
{"title":"Some Approximation Properties of Parametric Baskakov–Schurer–Szász Operators Through a Power Series Summability Method","authors":"N. Braha, Toufik Mansour, M. Mursaleen","doi":"10.1007/s11785-024-01510-8","DOIUrl":"https://doi.org/10.1007/s11785-024-01510-8","url":null,"abstract":"","PeriodicalId":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140357615","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}