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Semigroups of composition operators on the Besov spaces Besov空间上复合算子的半群
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-02-17 DOI: 10.1007/s43034-025-00411-x
Renyu Chen, Yali Dong
{"title":"Semigroups of composition operators on the Besov spaces","authors":"Renyu Chen,&nbsp;Yali Dong","doi":"10.1007/s43034-025-00411-x","DOIUrl":"10.1007/s43034-025-00411-x","url":null,"abstract":"<div><p>In this paper, we characterize the strong continuity of composition semigroups on analytic Besov spaces <span>(B_{p}(1&lt;p&lt;infty ).)</span> First, we show that every semigroup of composition operators <span>({C_{varphi _{t}}})</span> are strongly continuous on <span>(B_{p}(2le p&lt;infty ).)</span> However, we can find a semigroup <span>({varphi _t})</span> such that the induced composition operator <span>(C_{varphi _t})</span> is not even bounded on <span>(B_p(1&lt;p&lt;2).)</span> We contribute novel counterexamples grounded in the geometric properties of the image domain of Kœnigs function to illustrate this point. Moreover, we provide a sufficient condition ensuring the strong continuity of any semigroup of composition operators in <span>(B_{p}(1&lt;p&lt;infty ).)</span> Additionally, we establish that <span>({C_{varphi _{t}}})</span> is not uniformly continuous on <span>(B_{p}(1&lt;p&lt;infty ),)</span> unless <span>({varphi _{t}})</span> is trivial.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143430996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Superreflexive tensor product spaces 超自反张量积空间
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-02-08 DOI: 10.1007/s43034-025-00408-6
Abraham Rueda Zoca
{"title":"Superreflexive tensor product spaces","authors":"Abraham Rueda Zoca","doi":"10.1007/s43034-025-00408-6","DOIUrl":"10.1007/s43034-025-00408-6","url":null,"abstract":"<div><p>The aim of this note is to prove that, given two superreflexive Banach spaces <i>X</i> and <i>Y</i>, then <span>(Xwidehat{otimes }_pi Y)</span> is superreflexive if and only if either <i>X</i> or <i>Y</i> is finite-dimensional. In a similar way, we prove that <span>(Xwidehat{otimes }_varepsilon Y)</span> is superreflexive if and only if either <i>X</i> or <i>Y</i> is finite-dimensional.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-025-00408-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143370007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the exactness of groupoid crossed products 关于群拟交叉积的精确性
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-02-07 DOI: 10.1007/s43034-025-00409-5
Changyuan Gao
{"title":"On the exactness of groupoid crossed products","authors":"Changyuan Gao","doi":"10.1007/s43034-025-00409-5","DOIUrl":"10.1007/s43034-025-00409-5","url":null,"abstract":"<div><p>Let <span>(({mathcal {A}},G,alpha ))</span> be a separable groupoid <span>(C^*)</span>-dynamical system and <span>(C_0(G^{(0)},{mathcal {A}}))</span> the <span>(C^*)</span>-algebra of continuous sections that vanish at infinity. When <span>(({mathcal {A}},G,alpha ))</span> has the approximation property, we prove that the crossed product <span>({mathcal {A}}rtimes _{alpha ,r}G)</span> is exact if and only if <span>(C_0(G^{(0)},{mathcal {A}}))</span> is exact. In particular, if <i>G</i> is topologically amenable and <span>(C_0(G^{(0)},{mathcal {A}}))</span> is exact, then <span>({mathcal {A}}rtimes _{alpha ,r}G)</span> is exact.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361911","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","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 certain orthogonality of operators on (mathcal {B(H)}) 上的算子保持一定正交性的映射 (mathcal {B(H)})
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-02-07 DOI: 10.1007/s43034-025-00406-8
Jingzhou Han, Weijuan Shi, Guoxing Ji
{"title":"Maps preserving certain orthogonality of operators on (mathcal {B(H)})","authors":"Jingzhou Han,&nbsp;Weijuan Shi,&nbsp;Guoxing Ji","doi":"10.1007/s43034-025-00406-8","DOIUrl":"10.1007/s43034-025-00406-8","url":null,"abstract":"<div><p>Let <span>({mathcal {H}})</span> be a complex Hilbert space of dimension at least 3 and <span>(mathcal {B(H)})</span> the algebra of all bounded linear operators on <span>({mathcal {H}})</span>. For any <span>(A, Bin {mathcal {B}}({mathcal {H}}))</span>, <i>A</i> and <i>B</i> are said to be orthogonal if <span>(A^*B=0)</span>. In this paper, we establish the general form of orthogonality preserving bijections on <span>(mathcal {B(H)})</span>. Furthermore, we obtain a characterization of bijections <span>(varphi :mathcal {B(H)}rightarrow mathcal {B(H)})</span> satisfying <span>(varphi (A)bot (varphi (B)-varphi (C)))</span> if and only if <span>(Abot (B-C))</span> for any <span>(A,B,Cin mathcal {B(H)})</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143361912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Several unitarily invariant norm inequalities for matrices 矩阵的几个酉不变范数不等式
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-02-02 DOI: 10.1007/s43034-025-00407-7
Junjian Yang, Shengyan Ma
{"title":"Several unitarily invariant norm inequalities for matrices","authors":"Junjian Yang,&nbsp;Shengyan Ma","doi":"10.1007/s43034-025-00407-7","DOIUrl":"10.1007/s43034-025-00407-7","url":null,"abstract":"<div><p>In this short note, we obtain several inequalities for unitarily invariant norms which are generalizations of the results shown by Zou et al. [Linear Algebra Appl. 562 (2019) 154–162] and [J. Math. Inequal. 10 (2016) 1119–1122]. At the same time, we generalize a result by Audenaert [Oper. Matrices. 9 (2015) 475–479].</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143107932","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Factorization of Bloch mappings through a Hilbert space 希尔伯特空间中Bloch映射的分解
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-01-24 DOI: 10.1007/s43034-024-00404-2
M. G. Cabrera-Padilla, A. Jiménez-Vargas, D. Ruiz-Casternado
{"title":"Factorization of Bloch mappings through a Hilbert space","authors":"M. G. Cabrera-Padilla,&nbsp;A. Jiménez-Vargas,&nbsp;D. Ruiz-Casternado","doi":"10.1007/s43034-024-00404-2","DOIUrl":"10.1007/s43034-024-00404-2","url":null,"abstract":"<div><p>We introduce the concept of vector-valued holomorphic mappings on the complex unit disk that factor through a Hilbert space and state the main properties of the space formed by such Bloch mappings equipped with a natural norm: linearization, Bloch transposition, surjective and injective Banach ideal property, Kwapień-type characterization by Bloch domination, and duality.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The core operator on (M^{2}_{psi ,phi })-type submodules and (N^{2}_{psi ,phi })-type quotient modules over the bidisk biddisk上(M^{2}_{psi ,phi })型子模块和(N^{2}_{psi ,phi })型商模块的核心算子
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-01-20 DOI: 10.1007/s43034-024-00405-1
Anjian Xu, Dengping Zhang
{"title":"The core operator on (M^{2}_{psi ,phi })-type submodules and (N^{2}_{psi ,phi })-type quotient modules over the bidisk","authors":"Anjian Xu,&nbsp;Dengping Zhang","doi":"10.1007/s43034-024-00405-1","DOIUrl":"10.1007/s43034-024-00405-1","url":null,"abstract":"<div><p>Let <span>(H^{2}(mathbb {D}^{2}))</span> be the Hardy module over the bidisc, and <span>(M^{2}_{psi ,phi })</span> the submodule generated by <span>((psi (z)-phi (w))^{2})</span>, where <span>(psi )</span> and <span>(phi )</span> are two inner functions. Let <span>(N^{2}_{psi ,phi }=H^2(mathbb {D}^2)ominus M^{2}_{psi ,phi })</span> be the corresponding quotient module. The submodules and quotient modules are important objects in multivariable operator theory; Wu and Yu have shown that <span>(N^{2}_{psi ,phi })</span> is essential normal. In this paper, the core operator of the submodule <span>(M^{2}_{psi ,phi }=[(psi (z)-phi (w))^{2}])</span> is proved to be Hilbert–Schmidt, and its norm is computed. Furthermore, the Hilbert–Schmidt norms of the commutators <span>([S_{z}^{*},S_{z}])</span>, <span>([S_{z}^{*},S_{w}])</span> and <span>([S_{w}^{*},S_{w}])</span> on <span>(N^{2}_{psi ,phi })</span> are given.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 2","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142995081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Inheritance of certain comparison and divisibility properties for generalized tracially approximated C*-algebras 广义迹逼近C*-代数的某些比较和可除性质的继承
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-01-12 DOI: 10.1007/s43034-024-00399-w
Xiaochun Fang, Zhongli Wang
{"title":"Inheritance of certain comparison and divisibility properties for generalized tracially approximated C*-algebras","authors":"Xiaochun Fang,&nbsp;Zhongli Wang","doi":"10.1007/s43034-024-00399-w","DOIUrl":"10.1007/s43034-024-00399-w","url":null,"abstract":"<div><p>Let <span>(Omega )</span> be a class of C*-algebras with the <i>m</i>-comparison property (respectively, the <i>n</i>-almost divisibility property, the weakly (<i>k</i>, <i>n</i>)-divisibility property). We show that any infinite-dimensional simple unital C*-algebra in the class GTA<span>(Omega )</span> (the class of C*-algebras which can be generalized tracially approximated by the C*-algebras in <span>(Omega )</span>) has <i>m</i>-comparison (respectively, is <span>((2n+1))</span>-almost divisible, is weakly (<i>k</i>, 2<i>n</i>)-divisible).</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142963089","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Isometric automorphisms of some reflexive algebras 一些自反代数的等距自同构
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-01-09 DOI: 10.1007/s43034-024-00400-6
Zhujun Yang, Hongjie Chen
{"title":"Isometric automorphisms of some reflexive algebras","authors":"Zhujun Yang,&nbsp;Hongjie Chen","doi":"10.1007/s43034-024-00400-6","DOIUrl":"10.1007/s43034-024-00400-6","url":null,"abstract":"<div><p>We construct a class of subspace lattices <span>({mathcal {L}})</span> on a separable infinite dimensional Hilbert space <span>(mathcal {K})</span>. Let <span>({{,textrm{Alg},}}{mathcal {L}})</span> be the corresponding subspace lattice algebras. We show that every isometric automorphism of <span>({{,textrm{Alg},}}{mathcal {L}})</span> is spatial. We also show that <span>({{,textrm{Alg},}}{mathcal {L}})</span> are decomposable, and an operator in <span>({{,textrm{Alg},}}{mathcal {L}})</span> is single if and only if it is rank 1 under certain conditions.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142939283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Essential norm of Hankel operators on weighted Bergman spaces of strongly pseudoconvex domains 强伪凸域加权Bergman空间上Hankel算子的本质范数
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2025-01-08 DOI: 10.1007/s43034-024-00403-3
Zhicheng Zeng, Xiaofeng Wang, Jin Xia
{"title":"Essential norm of Hankel operators on weighted Bergman spaces of strongly pseudoconvex domains","authors":"Zhicheng Zeng,&nbsp;Xiaofeng Wang,&nbsp;Jin Xia","doi":"10.1007/s43034-024-00403-3","DOIUrl":"10.1007/s43034-024-00403-3","url":null,"abstract":"<div><p>Let <span>(rho )</span> be the defining function of a bounded strongly pseudoconvex domain <i>D</i> with smooth boundary in <span>({mathbb {C}}^n)</span>. In this paper, we study the essential norm of Hankel operators <span>(H^beta _f)</span> which are considered as operators from weighted Bergman spaces <span>(A^p(D,|rho |^alpha ,dV))</span> to <span>(L^q(D,|rho |^beta ,dV))</span> with <span>(1&lt;ple q&lt;infty )</span> and <span>(-1&lt;alpha ,beta &lt;infty )</span>. For <span>(fin L^1(D,|rho |^beta ,dV))</span>, we obtain some quantities in terms of the symbol function <i>f</i>, which are comparable to the essential norm of the Hankel operator <span>(H^beta _f)</span>. Furthermore, it is shown that the essential norm of <span>(H^beta _f)</span> is equivalent to the distance norm from itself to compact Hankel operators.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142938673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","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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