{"title":"On (hbox {w}^*)-Dunford–Pettis operators","authors":"Şafak Alpay, 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}
{"title":"Lip-linear operators and their connection to Lipschitz tensor products","authors":"Athmane Ferradi, 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}
{"title":"On Roth-type solvability criteria for generalized Sylvester matrix and operator equations","authors":"Hua Wang, Xiaoju Jin, 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}
{"title":"Weak characterizations of the Schur property","authors":"W. M. Ruess, 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}
{"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}
{"title":"Generalised Morrey sequence spaces","authors":"Dorothee D. Haroske, 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<ple u<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}
{"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<r<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}
Fernando Cobos, Luz M. Fernández-Cabrera, Antón Martínez
{"title":"Interpolation of the inner measure of bilinear operators by the real method","authors":"Fernando Cobos, Luz M. Fernández-Cabrera, 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}
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, Mohamed Amine Aouichaoui, 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}
{"title":"Extension of m-isometric weighted composition operators on directed graphs","authors":"V. Devadas, E. Shine Lal, 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}