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Advances in Operator Theory最新文献

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Multipliers between model spaces in non-Hilbertian setups 非希尔伯特设置中模型空间之间的乘数
IF 0.7
Advances in Operator Theory Pub Date : 2026-08-18 DOI: 10.1007/s43036-026-00531-8
Arun Kumar Bhardwaj, Arup Chattopadhyay, R. K. Srivastava
{"title":"Multipliers between model spaces in non-Hilbertian setups","authors":"Arun Kumar Bhardwaj,&nbsp;Arup Chattopadhyay,&nbsp;R. K. Srivastava","doi":"10.1007/s43036-026-00531-8","DOIUrl":"10.1007/s43036-026-00531-8","url":null,"abstract":"<div><p>Given a pair of inner functions <span>(Theta _1)</span> and <span>(Theta _2)</span> on the unit disk, and the corresponding inner functions <span>(I_1)</span> and <span>(I_2)</span> on the upper half-plane, the spaces of multipliers <span>(mathcal {M}^p(Theta _1, Theta _2))</span> and <span>(mathcal {M}^p(I_1, I_2))</span> between the corresponding model spaces have been studied. In contrast to the result <span>(mathcal {U}_infty mathcal {M}^2(Theta _1, Theta _2) = mathcal {M}^2(I_1, I_2))</span> obtained by Fricain, Hartmann, and Ross, we prove that this identity fails to hold if <span>(p ne 2)</span>. Furthermore, inspired by Crofoot’s work on surjective multipliers, we provide refined characterizations and new insights into the conditions under which equalities such as <span>(mathcal {M}^p(Theta _1, Theta _3) = mathcal {M}^p(Theta _2, Theta _3))</span> and <span>(mathcal {M}^p(Theta _1, Theta _2) = mathcal {M}^p(Theta _1, Theta _3))</span> hold.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782992","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
Dynamics of weighted shifts on generalized Hardy spaces of trees 广义Hardy树空间上的权移动力学
IF 0.7
Advances in Operator Theory Pub Date : 2026-08-17 DOI: 10.1007/s43036-026-00530-9
Xiang Chen, Li Zhang, Zehua Zhou
{"title":"Dynamics of weighted shifts on generalized Hardy spaces of trees","authors":"Xiang Chen,&nbsp;Li Zhang,&nbsp;Zehua Zhou","doi":"10.1007/s43036-026-00530-9","DOIUrl":"10.1007/s43036-026-00530-9","url":null,"abstract":"<div><p>In this paper, we study the dynamical properties of weighted backward shifts <span>(B_{lambda })</span> on the little generalized Hardy space on a rooted tree. More precisely, we provide a characterization of <span>(mathcal {F})</span>-transitivity for <span>(B_{lambda })</span>. In addition, we characterize weighted backward shifts on rooted directed trees that have an orbit with a nonzero limit point. Using these equivalent conditions, we construct several concrete examples illustrating different dynamical behaviors of weighted backward shifts.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782320","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 Fourier transform in variable exponent Lebesgue spaces 变指数勒贝格空间中的傅里叶变换
IF 0.7
Advances in Operator Theory Pub Date : 2026-08-13 DOI: 10.1007/s43036-026-00526-5
André Pedroso Kowacs, Wagner Augusto Almeida de Moraes
{"title":"The Fourier transform in variable exponent Lebesgue spaces","authors":"André Pedroso Kowacs,&nbsp;Wagner Augusto Almeida de Moraes","doi":"10.1007/s43036-026-00526-5","DOIUrl":"10.1007/s43036-026-00526-5","url":null,"abstract":"<div><p>In this work we define a Fourier transform for each <span>(fin L^{p(cdot )}({{,mathrm{mathbb {R}},}}))</span>, for a large class of exponent functions <span>(p(cdot ))</span>, as the distributional derivative of a Hölder continuous function. A norm is defined in the space of such Fourier transforms so that it is isometrically isomorphic to <span>(L^{p(cdot )}({{,mathrm{mathbb {R}},}}))</span>. We also prove several properties of this Fourier transform, such as inversion in norm and an exchange theorem.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-026-00526-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148752025","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
The numerical ranges of the generalized quadratic operators 广义二次算子的数值范围
IF 0.7
Advances in Operator Theory Pub Date : 2026-08-12 DOI: 10.1007/s43036-026-00525-6
Kangjian Wu, Qingxiang Xu
{"title":"The numerical ranges of the generalized quadratic operators","authors":"Kangjian Wu,&nbsp;Qingxiang Xu","doi":"10.1007/s43036-026-00525-6","DOIUrl":"10.1007/s43036-026-00525-6","url":null,"abstract":"<div><p>We investigate the generalized quadratic operator defined by </p><div><div><span>$$ T =left( begin{array}{cc} a I_H &amp; A c A^* &amp; bI_K end{array} right) ,$$</span></div></div><p>where <i>H</i> and <i>K</i> are Hilbert spaces, <span>(A:Krightarrow H)</span> is a bounded linear operator, <span>(I_H)</span> and <span>(I_K)</span> denote the identity operators on <i>H</i> and <i>K</i>, respectively, and <i>a</i>, <i>b</i>, <i>c</i> are complex numbers. It is shown that <i>T</i> attains its norm if and only if <i>A</i> attains its norm. Furthermore, a complete characterization of the numerical range of <i>T</i> is provided by a new approach.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751790","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
Fredholm operators on Hilbert modules Hilbert模上的Fredholm算子
IF 0.7
Advances in Operator Theory Pub Date : 2026-08-10 DOI: 10.1007/s43036-026-00528-3
Palanivel Manoharan
{"title":"Fredholm operators on Hilbert modules","authors":"Palanivel Manoharan","doi":"10.1007/s43036-026-00528-3","DOIUrl":"10.1007/s43036-026-00528-3","url":null,"abstract":"<div><p>Let A be a unital not necessarily commutative C*-algebra. In this manuscript, we define that a bounded adjointable operator between two Hilbert A-modules is a Fredholm operator if it has finitely generated projective kernel and cokernel as a straight forward generalization of the classical definition. We generalize the classical Atkinson theorem and a version of Atiyah–Janich theorem to show that the index holds the homotopy invariance property for this class of operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-026-00528-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751443","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
Wold-type decomposition and Beurling-type theorem for covariant representations 协变表示的世界型分解和beurling型定理
IF 0.7
Advances in Operator Theory Pub Date : 2026-08-06 DOI: 10.1007/s43036-026-00527-4
Dimple Saini, Azad Rohilla
{"title":"Wold-type decomposition and Beurling-type theorem for covariant representations","authors":"Dimple Saini,&nbsp;Azad Rohilla","doi":"10.1007/s43036-026-00527-4","DOIUrl":"10.1007/s43036-026-00527-4","url":null,"abstract":"<div><p>Using operator inequalities, we study a Wold-type decomposition of covariant representations. Building on this decomposition, we prove a Beurling-type theorem showing that every nonzero invariant subspace is uniquely determined by its wandering subspace. Our results extend classical theorems of Beurling and subsequent developments for left-invertible operators to the setting of covariant representations of <span>(C^*)</span>-correspondences, providing a unified framework for invariant subspace theory under operator inequalities.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148750982","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
Additive and multiplicative maps in norm on the positive cone of continuous function algebras 连续函数代数正锥上范数上的加性和乘性映射
IF 0.7
Advances in Operator Theory Pub Date : 2026-07-30 DOI: 10.1007/s43036-026-00521-w
Takeshi Miura, Natsumi Shibata
{"title":"Additive and multiplicative maps in norm on the positive cone of continuous function algebras","authors":"Takeshi Miura,&nbsp;Natsumi Shibata","doi":"10.1007/s43036-026-00521-w","DOIUrl":"10.1007/s43036-026-00521-w","url":null,"abstract":"<div><p>Let <i>X</i> and <i>Y</i> be locally compact Hausdorff spaces. We denote by <span>(C_0^+(X))</span> the cone of all non-negative real-valued continuous functions on <i>X</i> vanishing at infinity. In this paper, we consider a bijection <span>(T:C_0^+(X) rightarrow C_0^+(Y))</span> satisfying the following two norm conditions for all <span>(f, g in C_0^+(X))</span>: </p><div><div><span>$$ Vert T(f+g) Vert = Vert T(f)+T(g) Vert ,qquad Vert T(f cdot g) Vert = Vert T(f) cdot T(g) Vert . $$</span></div></div><p>The main result of this paper is that such a map <i>T</i> is a composition operator of the form <span>(T(f) = f circ tau )</span>, induced by a homeomorphism <span>(tau :Y rightarrow X)</span>. As a direct consequence of our main theorem, we obtain a positive cone version of the Gelfand–Kolmogoroff theorem.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"11 4","pages":""},"PeriodicalIF":0.7,"publicationDate":"2026-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148615081","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 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
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