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Advances in Operator Theory最新文献

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On a (C^*)-diagonal generated by the toric code 在由环面代码生成的(C^*) -对角线上
IF 0.7
Advances in Operator Theory Pub Date : 2026-07-14 DOI: 10.1007/s43036-026-00520-x
Danilo Polo Ojito, Emil Prodan
{"title":"On a (C^*)-diagonal generated by the toric code","authors":"Danilo Polo Ojito,&nbsp;Emil Prodan","doi":"10.1007/s43036-026-00520-x","DOIUrl":"10.1007/s43036-026-00520-x","url":null,"abstract":"<div><p>We study the abelian sub-<span>(C^*)</span>-algebra of the <span>(2^infty )</span>-UHF algebra generated by the star and face operators of Kitaev’s toric code. We show that it is a <span>(C^*)</span>-diagonal equivalent to the canonical diagonal of <span>(M_{2^infty })</span>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465127","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
Kippenhahn’s conjecture revisited Kippenhahn的猜想被重新审视
IF 0.7
Advances in Operator Theory Pub Date : 2026-07-14 DOI: 10.1007/s43036-026-00523-8
Michael Stessin
{"title":"Kippenhahn’s conjecture revisited","authors":"Michael Stessin","doi":"10.1007/s43036-026-00523-8","DOIUrl":"10.1007/s43036-026-00523-8","url":null,"abstract":"<div><p>In 1951 paper Kippenhahn conjectured that if the characteristic polynomial <span>(P_A(x_1,x_2,x_3)=text{ det }(x_1A_1+x_2A_2-x_3I),)</span> where <span>(A_1)</span> and <span>(A_2)</span> are <span>(ntimes n)</span> Hermitian matrices, has a repeated factor in the polynomial ring <span>({{mathbb {C}}}[x_1,x_2,x_3],)</span> then the pair <span>((A_1,A_2))</span> is unitary equivalent to a direct sum <span>((C_1oplus C_2, D_1oplus D_2))</span> where <span>(C_i, D_iin M_{n_i}({{mathbb {C}}}) )</span> for some <span>(1le n_i&lt;n, n_1+n_2=n, i=1,2.)</span> Kippenhahn verified the conjecture whenever the degree of the minimal polynomial of <span>(x_1A_1 + x_2A_2)</span> is 1 or 2. In subsequent 1982 works Shapiro obtained a number of results which supported the conjecture. In particular, she showed that it held if <span>(n le 5.)</span> In 1983 Laffey showed that, in general, Kippenhahn’s conjecture was not true by constructing a counterexample for <span>(n=8.)</span> Since then additional counterexamples were worked out. Some positive results in this direction including the quantum version of the conjecture were established as well. In this paper we use methods of recently developed local spectral analysis to give some necessary and sufficient conditions for the affirmative answer to Kippenhahn’s conjecture in terms of the characteristic polynomials of certain elements of the algebra generated by the matrices in the tuple.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465749","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
Dual valued quadratic derivable maps on (textbf{C}^*)-algebras (textbf{C}^*) -代数上的对偶值二次可导映射
IF 0.7
Advances in Operator Theory Pub Date : 2026-07-13 DOI: 10.1007/s43036-026-00524-7
Mohsen Niazi
{"title":"Dual valued quadratic derivable maps on (textbf{C}^*)-algebras","authors":"Mohsen Niazi","doi":"10.1007/s43036-026-00524-7","DOIUrl":"10.1007/s43036-026-00524-7","url":null,"abstract":"<div><p>We study mappings <span>(T)</span> from a unital <span>(mathrm C^*)</span>-algebra <span>(A)</span> into its dual space, <span>(A^*)</span>, which satisfy the ternary derivation identity with respect to the quadratic Jordan product. We prove that whenever <span>(A)</span> admits a projection <span>(p)</span> that is Murray–von Neumann equivalent to <span>(1-p)</span>, such mappings are automatically additive and conjugate homogeneous over <span>(mathbb {Q}+imathbb {Q})</span>, and they become ternary derivations when they are continuous.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466000","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
Some special geometric configurations of the eigenvalues of matrices 矩阵特征值的一些特殊几何构型
IF 0.7
Advances in Operator Theory Pub Date : 2026-07-13 DOI: 10.1007/s43036-026-00519-4
Rajesh Sharma, Vijay Sharma
{"title":"Some special geometric configurations of the eigenvalues of matrices","authors":"Rajesh Sharma,&nbsp;Vijay Sharma","doi":"10.1007/s43036-026-00519-4","DOIUrl":"10.1007/s43036-026-00519-4","url":null,"abstract":"<div><p>We obtain some conditions under which all the eigenvalues of a matrix lie at the vertices of a regular polygon. We also consider the case when the eigenvalues lie at the vertices of two concyclic regular polygons. The special cases yield some interesting results about the eigenvalues of unitary matrices and their geometric configurations. Some results related to the similarity of two unitary matrices are also given here.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148466012","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
Difference of weighted composition operators from (alpha )-weighted space to radially (omega )-weighted space in the unit ball 单位球中从(alpha ) -加权空间到径向(omega ) -加权空间的加权组合算子的差异
IF 0.7
Advances in Operator Theory Pub Date : 2026-07-09 DOI: 10.1007/s43036-026-00517-6
Cui Chen, Wei Lu, Li Zhang
{"title":"Difference of weighted composition operators from (alpha )-weighted space to radially (omega )-weighted space in the unit ball","authors":"Cui Chen,&nbsp;Wei Lu,&nbsp;Li Zhang","doi":"10.1007/s43036-026-00517-6","DOIUrl":"10.1007/s43036-026-00517-6","url":null,"abstract":"<div><p>In this paper, we study the difference of weighted composition operators acting from the <span>(alpha )</span>-weighted space to radially <span>(omega )</span>-weighted space over the unit ball of <span>(mathbb {C}^m)</span>. We present equivalent characterizations for its boundedness, derive corresponding estimation formulas for its essential norm, and thereby provide equivalent descriptions for its compactness.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465537","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 polar decomposition of closed linear relations and its applications 封闭线性关系的极坐标分解及其应用
IF 0.7
Advances in Operator Theory Pub Date : 2026-07-09 DOI: 10.1007/s43036-026-00522-9
Mohamed Amine Aouichaoui, Zied Garbouj
{"title":"The polar decomposition of closed linear relations and its applications","authors":"Mohamed Amine Aouichaoui,&nbsp;Zied Garbouj","doi":"10.1007/s43036-026-00522-9","DOIUrl":"10.1007/s43036-026-00522-9","url":null,"abstract":"<div><p>The purpose of this paper is to revisit the polar decomposition theorem for closed everywhere defined linear relations and to illustrate some of its applications. In doing so, we extend Furuta’s results and those of Ito, Yamazaki, and Yanagida, which were previously established for operators, to the realm of closed linear relations. Additionally, we propose potential directions for future research, such as extending the theoretical framework to include <i>C</i>-polar decomposition for closed linear relations, further studying weak-type normal linear relations, and investigating inequalities for closed linear relations components. These developments significantly broaden the scope of polar decomposition theory and open new avenues for further exploration.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465536","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 unbounded complementable operators 关于无界互补算子
IF 0.7
Advances in Operator Theory Pub Date : 2026-06-22 DOI: 10.1007/s43036-026-00516-7
Sachin Manjunath Naik, P. Sam Johnson
{"title":"On unbounded complementable operators","authors":"Sachin Manjunath Naik,&nbsp;P. Sam Johnson","doi":"10.1007/s43036-026-00516-7","DOIUrl":"10.1007/s43036-026-00516-7","url":null,"abstract":"<div><p>The concept of complementability is extended from bounded operators to densely defined operators on Hilbert spaces. By introducing appropriate projections and decomposition techniques, a framework is developed for analyzing complementability in this broader context. The results provide new insights into the structure of unbounded operators, contributing to the ongoing development of operator theory.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-026-00516-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323077","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
Complex symmetric Toeplitz operators through representation theory tools 通过表示理论工具实现复对称Toeplitz算子
IF 0.7
Advances in Operator Theory Pub Date : 2026-06-22 DOI: 10.1007/s43036-026-00518-5
Esteban Heredia-Muñoz, Armando Sánchez-Nungaray, Carlos-Hugo Jiménez-Gómez
{"title":"Complex symmetric Toeplitz operators through representation theory tools","authors":"Esteban Heredia-Muñoz,&nbsp;Armando Sánchez-Nungaray,&nbsp;Carlos-Hugo Jiménez-Gómez","doi":"10.1007/s43036-026-00518-5","DOIUrl":"10.1007/s43036-026-00518-5","url":null,"abstract":"<div><p>Proceeding through a representation theoretic approach, we study the family of Toeplitz operators on the weighted Bergman space <span>(mathcal {H}^2_{alpha }(mathbb {B}_n))</span> whose symbols are invariant under the action of the semidirect group <span>(S_{Delta } rtimes mathbb {T}^{n})</span>, where <span>(S_{Delta })</span> is a subgroup of permutations. Associating a suitable partition <span>(Delta )</span> we associated the conjugation <span>(J_{A})</span> on the Bergman space. Moreover we characterize the complex symmetric Toeplitz operators <span>(T_{a})</span> and <span>(T_{a(r)t^{p}overline{t}^{q}})</span> with respect the conjugation <span>(J_A)</span>, where the symbols are invariant under the action of <span>(S_{Delta } rtimes mathbb {T}^{n})</span>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-026-00518-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323452","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
Commuting Hankel and Toeplitz operators on the Hardy space of the bidisk 双盘Hardy空间上的交换Hankel算子和Toeplitz算子
IF 0.7
Advances in Operator Theory Pub Date : 2026-06-18 DOI: 10.1007/s43036-026-00513-w
Hong Zou, Tao Yu
{"title":"Commuting Hankel and Toeplitz operators on the Hardy space of the bidisk","authors":"Hong Zou,&nbsp;Tao Yu","doi":"10.1007/s43036-026-00513-w","DOIUrl":"10.1007/s43036-026-00513-w","url":null,"abstract":"<div><p>In this paper, we establish a necessary and sufficient condition for a Toeplitz operator with a bounded pluriharmonic symbol to commute with a Hankel operator with a bounded symbol on the Hardy space of the bidisk.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281123","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
Maps preserving the (partial )-spectrum of skew products of operators 保留算子的偏积(partial ) -谱的映射
IF 0.7
Advances in Operator Theory Pub Date : 2026-06-15 DOI: 10.1007/s43036-026-00515-8
Hassane Benbouziane, Aukacha Daoudi, Mustapha Ech-Chérif El Kettani, Ismail El Khchin
{"title":"Maps preserving the (partial )-spectrum of skew products of operators","authors":"Hassane Benbouziane,&nbsp;Aukacha Daoudi,&nbsp;Mustapha Ech-Chérif El Kettani,&nbsp;Ismail El Khchin","doi":"10.1007/s43036-026-00515-8","DOIUrl":"10.1007/s43036-026-00515-8","url":null,"abstract":"<div><p>Let <span>(mathcal {B}(mathcal {H}))</span> be the algebra of all bounded linear operators on an infinite-dimensional Hilbert space <span>(mathcal {H})</span>. A map <span>(Delta )</span>, from <span>( mathcal {B}(mathcal {H}) )</span> into a closed subset of <span>( mathbb {C} )</span> is said to be a <span>(partial )</span>-spectrum if <span>(partial sigma (T) subseteq Delta (T) subseteq sigma (T))</span> for all <span>(T in mathcal {B}(mathcal {H}))</span>, where <span>(sigma (T))</span> denotes the spectrum of <i>T</i> and <span>(partial sigma (T))</span> its boundary. Fix a <span>(partial )</span>-spectrum map <span>(Delta )</span>. In this paper, we characterize all maps <span>(phi :mathcal {B}(mathcal {H}) rightarrow mathcal {B}(mathcal {H}))</span> whose ranges contain all operators of rank at most two and that satisfy either <span>(Delta (TS^*) = Delta big (phi (T)phi (S)^*big ))</span> for all <span>(T,S in mathcal {B}(mathcal {H}))</span> or <span>(Delta (TS^*T) = Delta big (phi (T)phi (S)^*phi (T)big ))</span> for all <span>(T,S in mathcal {B}(mathcal {H}).)</span></p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 3","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281017","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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