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Advances in Operator Theory最新文献

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Frame dimension functions of g-frames g-框架的框架维函数
IF 0.7
Advances in Operator Theory Pub Date : 2026-04-07 DOI: 10.1007/s43036-026-00502-z
Tian Wang, Miao He
{"title":"Frame dimension functions of g-frames","authors":"Tian Wang,&nbsp;Miao He","doi":"10.1007/s43036-026-00502-z","DOIUrl":"10.1007/s43036-026-00502-z","url":null,"abstract":"<div><p>Frame theory has important applications in phase-retrieval problem, and the dimension function of a frame can serve as a candidate for measuring its phase retrievability. In this paper, we first investigate the relationship between phase retrievability and the dimension function of g-frames incorporating operator theory. We find that the dimension function of a phase-retrievable g-frame closely aligns with that of an ordinary frame. This consistency suggests that the dimension function of a g-frame can likewise act as a metric for measuring its phase retrieval capability. Specifically, we find that the exact PR-redundancy of a g-frame is equivalent to the exactness of its dimension function. The paper then investigates the structure of the dimension function range of g-frames. We find that, even when the number of operators in a g-frame is not less than <i>n</i>, significant differences remain from the case of ordinary frames regarding the structure of the dimension function range of g-Riesz basis and whether the range contains <i>n</i>. Finally, we present a method for examining the dimension function of a g-frame via its induced frame, along with a straightforward approach to construct g-frames whose dimension function range contains <i>n</i>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-04-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147642412","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 forward and backward shift on the Zygmund space of a tree 树的齐格蒙空间上的向前和向后移动
IF 0.7
Advances in Operator Theory Pub Date : 2026-03-30 DOI: 10.1007/s43036-026-00501-0
Itzama Delgadillo-García, Rubén A. Martínez-Avendaño
{"title":"The forward and backward shift on the Zygmund space of a tree","authors":"Itzama Delgadillo-García,&nbsp;Rubén A. Martínez-Avendaño","doi":"10.1007/s43036-026-00501-0","DOIUrl":"10.1007/s43036-026-00501-0","url":null,"abstract":"<div><p>The Zygmund space of a tree is the Banach space of complex-valued functions defined on the vertices of a rooted infinite and locally-finite tree such that their second discrete derivative is bounded. In this paper we study the forward and backward shift operators on the Zygmund space of a tree. We show that the forward shift operator is always bounded on the Zygmund space, and we find its norm and spectrum. We give necessary and sufficient conditions for the backward shift operator to be bounded, and give an estimate for its norm. In the case the tree is homogeneous, we give an exact expression for the norm of the backward shift operator and we find its spectrum. The results in the paper also apply verbatim to the little Zygmund space.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147607007","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 complete asymptotic expansion for the semi-exponential Post–Widder operators 半指数后widder算子的完全渐近展开式
IF 0.7
Advances in Operator Theory Pub Date : 2026-03-24 DOI: 10.1007/s43036-026-00499-5
Ulrich Abel, Octavian Agratini, Radu Păltănea
{"title":"A complete asymptotic expansion for the semi-exponential Post–Widder operators","authors":"Ulrich Abel,&nbsp;Octavian Agratini,&nbsp;Radu Păltănea","doi":"10.1007/s43036-026-00499-5","DOIUrl":"10.1007/s43036-026-00499-5","url":null,"abstract":"<div><p>In the present paper, we study the asymptotic properties of the semi-exponential Post–Widder operator. It is connected with the power function <i>p</i>, <span>(pleft( xright) =x^{2})</span>. The main result is a pointwise complete asymptotic expansion valid for locally smooth functions of exponential growth. All coefficients are derived and explicitly given. As a special case we recover the complete asymptotic expansion for the classical Post–Widder operator.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-026-00499-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561640","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
Local symmetry and smoothness in the space of vector-valued continuous functions 向量值连续函数空间的局部对称性和光滑性
IF 0.7
Advances in Operator Theory Pub Date : 2026-03-16 DOI: 10.1007/s43036-026-00500-1
Mohit, Ranjana Jain
{"title":"Local symmetry and smoothness in the space of vector-valued continuous functions","authors":"Mohit,&nbsp;Ranjana Jain","doi":"10.1007/s43036-026-00500-1","DOIUrl":"10.1007/s43036-026-00500-1","url":null,"abstract":"<div><p>In this article, we characterize the left symmetric points in <i>C</i>(<i>K</i>, <i>X</i>), where <i>K</i> is a compact Hausdorff space and <i>X</i> is a Banach space. We also provide necessary and sufficient conditions for the right symmetric points in <i>C</i>(<i>K</i>, <i>X</i>). Further, we identify the smooth points in the space <span>(C_0(K,X))</span>, <i>K</i> being locally compact Hausdorff space and <i>X</i> being a Banach space.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147559753","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 new characterization for the essential norm of weighted composition operators and their differences on weighted Bergman spaces 加权复合算子本质范数的新表征及其在加权Bergman空间上的差异
IF 0.7
Advances in Operator Theory Pub Date : 2026-02-24 DOI: 10.1007/s43036-026-00497-7
Kobra Esmaeili
{"title":"A new characterization for the essential norm of weighted composition operators and their differences on weighted Bergman spaces","authors":"Kobra Esmaeili","doi":"10.1007/s43036-026-00497-7","DOIUrl":"10.1007/s43036-026-00497-7","url":null,"abstract":"<div><p>We investigate the essential norms of weighted composition operators and the differences of such operators acting between weighted Bergman spaces <span>(mathcal {A}_{omega }^{p})</span>, with a focus on almost standard radial weights. Motivated by the complexity of existing approaches that depend extensively on Carleson measures, we derive easily computable criteria for the compactness of weighted composition operators. Consequently, these criteria yield explicit estimates for the essential norms of such operators, and of their differences, including both lower and upper bounds, improving the best known bounds.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147341287","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
Two-sided remotely almost periodic solutions of ordinary differential equations in Banach spaces Banach空间中常微分方程的双边远概周期解
IF 0.7
Advances in Operator Theory Pub Date : 2026-02-21 DOI: 10.1007/s43036-026-00496-8
David Cheban
{"title":"Two-sided remotely almost periodic solutions of ordinary differential equations in Banach spaces","authors":"David Cheban","doi":"10.1007/s43036-026-00496-8","DOIUrl":"10.1007/s43036-026-00496-8","url":null,"abstract":"<div><p>The aim of this paper is to study the two-sided remotely almost periodic solutions of ordinary differential equations in Banach spaces of the form <span>(x'=A(t)x+f(t)+F(t,x))</span> with two-sided remotely almost periodic coefficients if the linear equation <span>(x'=A(t)x)</span> satisfies the condition of exponential trichotomy and nonlinearity <i>F</i> is \"small\".</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147340905","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
On quotients of ideals of weighted holomorphic mappings 关于加权全纯映射的理想商
IF 0.7
Advances in Operator Theory Pub Date : 2026-02-04 DOI: 10.1007/s43036-025-00493-3
Amar Belacel, Amar Bougoutaia, Pilar Rueda
{"title":"On quotients of ideals of weighted holomorphic mappings","authors":"Amar Belacel,&nbsp;Amar Bougoutaia,&nbsp;Pilar Rueda","doi":"10.1007/s43036-025-00493-3","DOIUrl":"10.1007/s43036-025-00493-3","url":null,"abstract":"<div><p>We explore the procedure given by left-hand quotients in the context of weighted holomorphic ideals. On the one hand, we show that this procedure does not generate new ideals other than the ideal of weighted holomorphic mappings when considering the left-hand quotients induced by the ideals of <i>p</i>-compact, weakly <i>p</i>-compact, unconditionally <i>p</i>-compact, approximable or right <i>p</i>-nuclear operators with their respective weighted holomorphic ideals. On the other hand, the procedure is of interest when considering other operators ideals as it provides new weighted holomorphic ideals. This is the case of the ideal of Grothendieck weighted holomorphic mappings or the ideal of Rosenthal weighted holomorphic mappings, where the applicability of this construction is shown.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00493-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336699","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
Fractional Kirchhoff systems in Musielak–Sobolev spaces: multiple weak solutions Musielak-Sobolev空间中的分数阶Kirchhoff系统：多重弱解
IF 0.7
Advances in Operator Theory Pub Date : 2026-02-04 DOI: 10.1007/s43036-025-00494-2
Mohammed Allou, Elhoussine Azroul, Mohammed Srati
{"title":"Fractional Kirchhoff systems in Musielak–Sobolev spaces: multiple weak solutions","authors":"Mohammed Allou,&nbsp;Elhoussine Azroul,&nbsp;Mohammed Srati","doi":"10.1007/s43036-025-00494-2","DOIUrl":"10.1007/s43036-025-00494-2","url":null,"abstract":"<div><p>We analyze nonlocal Kirchhoff systems in fractional Musielak–Sobolev spaces. By means of Ricceri’s theorem, it is established that the system possesses weak solutions under fairly general conditions for the modular, the Kirchhoff functions, and the nonlinearities. Additionally, a case of growth of the logarithmic type is presented to visualize the outcome.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336700","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
Best m-term trigonometric approximation in weighted Wiener spaces and applications 加权Wiener空间中的最佳m项三角逼近及其应用
IF 0.7
Advances in Operator Theory Pub Date : 2026-01-27 DOI: 10.1007/s43036-025-00480-8
Moritz Moeller, Serhii Stasyuk, Tino Ullrich
{"title":"Best m-term trigonometric approximation in weighted Wiener spaces and applications","authors":"Moritz Moeller,&nbsp;Serhii Stasyuk,&nbsp;Tino Ullrich","doi":"10.1007/s43036-025-00480-8","DOIUrl":"10.1007/s43036-025-00480-8","url":null,"abstract":"<div><p>In this paper we study best <i>m</i>-term trigonometric approximation in weighted Wiener spaces and its consequences for Besov and Sobolev spaces with bounded mixed derivative/difference. We obtain several sharp asymptotic bounds for weighted Wiener spaces including the quasi-Banach case. It has recently been observed that best <i>m</i>-term trigonometric widths in the uniform norm together with recovery algorithms stemming from compressed sensing serve to control the optimal sampling recovery error in various relevant spaces of multivariate functions. We use a collection of old and new tools as well as novel findings to extend the recovery bounds to classical multivariate smoothness spaces. It turns out that embeddings into Wiener spaces serve as a powerful tool to improve certain recent bounds.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00480-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146082765","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
Li–Yorke and expansive composition operators on rearrangement invariant spaces 重排不变空间上的Li-Yorke和扩展复合算子
IF 0.7
Advances in Operator Theory Pub Date : 2026-01-20 DOI: 10.1007/s43036-025-00495-1
Romesh Kumar, Rajat Singh
{"title":"Li–Yorke and expansive composition operators on rearrangement invariant spaces","authors":"Romesh Kumar,&nbsp;Rajat Singh","doi":"10.1007/s43036-025-00495-1","DOIUrl":"10.1007/s43036-025-00495-1","url":null,"abstract":"<div><p>The main aim of this paper is to study Li–Yorke and Expansive composition operators on rearrangement-invariant Banach function spaces.\u0000</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145996593","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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