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Advances in Operator Theory最新文献

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A note on (L^p)-(L^q) boundedness of Fourier multipliers on noncommutative spaces 关于非交换空间上傅里叶乘子的(L^p) - (L^q)有界性的注记
IF 0.8
Advances in Operator Theory Pub Date : 2025-04-08 DOI: 10.1007/s43036-025-00436-y
Michael Ruzhansky, Kanat Tulenov
{"title":"A note on (L^p)-(L^q) boundedness of Fourier multipliers on noncommutative spaces","authors":"Michael Ruzhansky,&nbsp;Kanat Tulenov","doi":"10.1007/s43036-025-00436-y","DOIUrl":"10.1007/s43036-025-00436-y","url":null,"abstract":"<div><p>In this work, we study Fourier multipliers on noncommutative spaces. In particular, we show a simple proof of <span>(L^p)</span>-<span>(L^q)</span> estimate of Fourier multipliers on general noncommutative spaces associated with semifinite von Neumann algebras. This includes the case of Fourier multipliers on general locally compact unimodular groups.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00436-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793267","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
Approximate Roberts directional orthogonalities 近似罗伯茨方向正交
IF 0.8
Advances in Operator Theory Pub Date : 2025-03-29 DOI: 10.1007/s43036-025-00433-1
Kallal Pal, Sumit Chandok
{"title":"Approximate Roberts directional orthogonalities","authors":"Kallal Pal,&nbsp;Sumit Chandok","doi":"10.1007/s43036-025-00433-1","DOIUrl":"10.1007/s43036-025-00433-1","url":null,"abstract":"<div><p>We define two types of approximate Roberts orthogonality with direction in the framework of a complex normed space. We examine their geometrical properties and demonstrate that the notion of <span>(epsilon )</span>-approximate directional orthogonality is weaker than that of <span>(epsilon )</span>-approximate orthogonality. Concerning the approximate Birkhoff orthogonality, we talk about the connection between them. Also, we provide the notion of an approximation Roberts directional orthogonality set and analyze the geometric characteristics of these sets. Furthermore, we discuss approximate orthogonality preserving mapping.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143735427","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
New estimates for numerical radius in (C^*)-algebras (C^*) -代数中数值半径的新估计
IF 0.8
Advances in Operator Theory Pub Date : 2025-03-25 DOI: 10.1007/s43036-025-00434-0
Ali Zamani
{"title":"New estimates for numerical radius in (C^*)-algebras","authors":"Ali Zamani","doi":"10.1007/s43036-025-00434-0","DOIUrl":"10.1007/s43036-025-00434-0","url":null,"abstract":"<div><p>Several numerical radius inequalities in the framework of <span>(C^*)</span>-algebras are proved in this paper. These results, which are based on an extension of the Buzano inequality for elements in a pre-Hilbert <span>(C^*)</span>-module, generalize earlier numerical radius inequalities. An expression for the <span>(C^*)</span>-algebra-valued norm based on the numerical radius is also given.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143698486","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
Remarks on non-homogeneous Cauchy problems with time-dependent generators 关于随时间变化的非均质 Cauchy 问题的评论
IF 0.8
Advances in Operator Theory Pub Date : 2025-03-24 DOI: 10.1007/s43036-025-00435-z
Pedro Marín-Rubio, Paulo N. Seminario-Huertas
{"title":"Remarks on non-homogeneous Cauchy problems with time-dependent generators","authors":"Pedro Marín-Rubio,&nbsp;Paulo N. Seminario-Huertas","doi":"10.1007/s43036-025-00435-z","DOIUrl":"10.1007/s43036-025-00435-z","url":null,"abstract":"<div><p>In this paper it is studied the well-posedness in several senses for non-homogeneous Cauchy problems where the infinitesimal generator depends on the time parameter. More specifically, we analyze the existence of classical, mild and weak solutions and their relationships. Thanks to uniqueness arguments, mild solutions are proved to satisfy a classical variational formulation. Finally, these results are applied to a thermoelastic plate model where the thermal part is of Cattaneo type and all the physical coefficients depend on time.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00435-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688269","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
Inequalities among the nth residual relative operator entropies 第n个残差相对算子熵之间的不等式
IF 0.8
Advances in Operator Theory Pub Date : 2025-03-22 DOI: 10.1007/s43036-025-00431-3
Hiroaki Tohyama, Eizaburo Kamei, Masayuki Watanabe
{"title":"Inequalities among the nth residual relative operator entropies","authors":"Hiroaki Tohyama,&nbsp;Eizaburo Kamei,&nbsp;Masayuki Watanabe","doi":"10.1007/s43036-025-00431-3","DOIUrl":"10.1007/s43036-025-00431-3","url":null,"abstract":"<div><p>We showed two types of operator inequalities between the <span>((n+1))</span>th residual relative operator entropy and the difference of the <i>n</i>th residual relative operator entropies. They are similar partially but have some differences. We investigate what these differences come from. Inequalities other than the previous ones are given through this process.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676478","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
An approach to root functions of matrix polynomials with applications in differential equations and meromorphic matrix functions 矩阵多项式的根函数及其在微分方程和亚纯矩阵函数中的应用
IF 0.8
Advances in Operator Theory Pub Date : 2025-03-21 DOI: 10.1007/s43036-025-00432-2
Muhamed Borogovac
{"title":"An approach to root functions of matrix polynomials with applications in differential equations and meromorphic matrix functions","authors":"Muhamed Borogovac","doi":"10.1007/s43036-025-00432-2","DOIUrl":"10.1007/s43036-025-00432-2","url":null,"abstract":"<div><p>First, we present a method for obtaining a canonical set of root functions and Jordan chains of the invertible matrix polynomial <i>L</i>(<i>z</i>) through elementary transformations of the matrix <i>L</i>(<i>z</i>) alone. This method provides a new and simple approach to deriving a general solution of the system of ordinary linear differential equations <span>(Lleft( frac{d}{dt}right) u=0)</span>, where <i>u</i>(<i>t</i>) is <i>n</i>-dimensional unknown function. We illustrate the effectiveness of this method by applying it to solve a high-order linear system of ODEs. Second, given a matrix generalized Nevanlinna function <span>(Qin N_{kappa }^{n times n})</span>, that satisfies certain conditions at <span>(infty )</span>, and a canonical set of root functions of <span>(hat{Q}(z):= -Q(z)^{-1})</span>, we construct the corresponding Pontryagin space <span>((mathcal {K}, [.,.]))</span>, a self-adjoint operator <span>(A:mathcal {K}rightarrow mathcal {K})</span>, and an operator <span>(Gamma : mathbb {C}^{n}rightarrow mathcal {K})</span>, that represent the function <i>Q</i>(<i>z</i>) in a Krein–Langer type representation. We illustrate the application of main results with examples involving concrete matrix polynomials <i>L</i>(<i>z</i>) and their inverses, defined as <span>(Q(z):=hat{L}(z):= -L(z)^{-1})</span>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00432-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143668363","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
2-Local automorphisms and derivations of triangular matrices 三角矩阵的2-局部自同构与导数
IF 0.8
Advances in Operator Theory Pub Date : 2025-03-18 DOI: 10.1007/s43036-025-00430-4
Wenbo Huang, Shan Li
{"title":"2-Local automorphisms and derivations of triangular matrices","authors":"Wenbo Huang,&nbsp;Shan Li","doi":"10.1007/s43036-025-00430-4","DOIUrl":"10.1007/s43036-025-00430-4","url":null,"abstract":"<div><p>Let <span>(mathcal {T})</span> denote the algebra of all <span>(2 times 2)</span> upper triangular matrices over a field <span>(mathbb {F})</span>. We show that the linear space of all 2-local derivations on <span>(mathcal {T})</span> decomposes as <span>(mathcal {L} = mathcal {D} oplus mathcal {L}_0)</span>, where <span>(mathcal {D})</span> is the subspace of all derivations, and <span>(mathcal {L}_0)</span> consists of 2-local derivations vanishing on a subset of <span>(mathcal {T})</span>, isomorphic to the space of functions <span>(f:mathbb {F}rightarrow mathbb {F})</span> such that <span>(f(0)=0)</span>. For any 2-local automorphism <span>(Lambda )</span> on <span>(mathcal {T})</span>, we show that there exists a unique automorphism <span>(phi )</span> and a 2-local automorphism <span>(Lambda _{1} in varPsi )</span> such that <span>(Lambda = phi Lambda _1)</span>, where <span>(varPsi )</span> is the monoid of 2-local automorphisms that act as the identity on a subset of <span>(mathcal {T})</span>. Furthermore, we establish that <span>(varPsi )</span> is isomorphic to the monoid of injective functions from <span>(mathbb {F}^{*})</span> to itself.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638424","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
DW-DP operators and DW-limited operators on Banach lattices Banach格上的DW-DP算子和dw -有限算子
IF 0.8
Advances in Operator Theory Pub Date : 2025-03-08 DOI: 10.1007/s43036-025-00429-x
Jin Xi Chen, Jingge Feng
{"title":"DW-DP operators and DW-limited operators on Banach lattices","authors":"Jin Xi Chen,&nbsp;Jingge Feng","doi":"10.1007/s43036-025-00429-x","DOIUrl":"10.1007/s43036-025-00429-x","url":null,"abstract":"<div><p>This paper is devoted to the study of two classes of operators related to disjointly weakly compact sets, which we call <i>DW</i>-DP operators and <i>DW</i>-limited operators, respectively. They carry disjointly weakly compact sets in a Banach lattice onto Dunford–Pettis sets and limited sets, respectively. We show that <i>DW</i>-DP (resp. <i>DW</i>-limited) operators are precisely those operators which are both weak Dunford–Pettis and order Dunford–Pettis (resp. weak<span>(^*)</span> Dunford–Pettis and order limited) operators. Furthermore, the approximation properties of positive <i>DW</i>-DP and positive <i>DW</i>-limited operators are given.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00429-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143581144","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
Chernoff’s product formula: Semigroup approximations with non-uniform time intervals Chernoff乘积公式：具有非均匀时间间隔的半群近似
IF 0.8
Advances in Operator Theory Pub Date : 2025-03-02 DOI: 10.1007/s43036-025-00428-y
József Zsolt Bernád, Andrew B. Frigyik
{"title":"Chernoff’s product formula: Semigroup approximations with non-uniform time intervals","authors":"József Zsolt Bernád,&nbsp;Andrew B. Frigyik","doi":"10.1007/s43036-025-00428-y","DOIUrl":"10.1007/s43036-025-00428-y","url":null,"abstract":"<div><p>Often, when we consider the time evolution of a system, we resort to approximation: Instead of calculating the exact orbit, we divide the time interval in question into uniform segments. Chernoff’s results in this direction provide us with a general approximation scheme. There are situations when we need to break the interval into uneven pieces. In this paper, we explore alternative conditions to the one found by Smolyanov <i>et al</i>. such that Chernoff’s original result can be extended to unevenly distributed time intervals. Two applications concerning the foundations of quantum mechanics and the central limit theorem are presented.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00428-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143527628","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
Paired kernels and truncated Toeplitz operators 成对核和截断的Toeplitz运算符
IF 0.8
Advances in Operator Theory Pub Date : 2025-02-27 DOI: 10.1007/s43036-025-00426-0
M. Cristina Câmara, Jonathan R. Partington
{"title":"Paired kernels and truncated Toeplitz operators","authors":"M. Cristina Câmara,&nbsp;Jonathan R. Partington","doi":"10.1007/s43036-025-00426-0","DOIUrl":"10.1007/s43036-025-00426-0","url":null,"abstract":"<div><p>This paper considers paired operators in the context of the Lebesgue Hilbert space <span>(L^2)</span> on the unit circle and its subspace, the Hardy space <span>(H^2.)</span> The kernels of such operators, together with their analytic projections, which are generalizations of Toeplitz kernels, are studied. Inclusion relations between such kernels are considered in detail, and the results are applied to describing the kernels of finite-rank asymmetric truncated Toeplitz operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00426-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143496980","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
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