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Cyclic vectors in Fock-type spaces in multi-variable case 多变量情况下 Fock 型空间中的循环向量
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-02-19 DOI: 10.1007/s43034-024-00323-2
Hansong Huang, Kou Hei Izuchi
{"title":"Cyclic vectors in Fock-type spaces in multi-variable case","authors":"Hansong Huang,&nbsp;Kou Hei Izuchi","doi":"10.1007/s43034-024-00323-2","DOIUrl":"10.1007/s43034-024-00323-2","url":null,"abstract":"<div><p>This manuscript concerns with cyclic vectors in the Fock-type spaces <span>({L^{p}_{a}}(mathbb C^d,s,alpha ))</span> of multi-variable cases, with positive parameters <span>(s,alpha )</span> and <span>(pge 1)</span>. The one-variable case has been settled by the authors. Here, it is shown that for a positive number <span>(snot in mathbb {N})</span>, a function <i>f</i> in the Fock-type space <span>({L^{p}_{a}}(mathbb C^d,s,alpha ))</span> is cyclic if and only if <i>f</i> is non-vanishing. However, the case of <i>s</i> being a positive integer turns out to be more complicated. Different techniques and methods are developed in multi-variable cases for a complete characterization of cyclic vectors in <span>({L^{p}_{a}}(mathbb C^d,s,alpha ))</span> for positive integers <i>s</i>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139903045","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
Regularity results for classes of Hilbert C*-modules with respect to special bounded modular functionals 关于特殊有界模态函数的希尔伯特 C* 模块类的正则性结果
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-02-17 DOI: 10.1007/s43034-024-00320-5
Michael Frank
{"title":"Regularity results for classes of Hilbert C*-modules with respect to special bounded modular functionals","authors":"Michael Frank","doi":"10.1007/s43034-024-00320-5","DOIUrl":"10.1007/s43034-024-00320-5","url":null,"abstract":"<div><p>Considering the deeper reasons of the appearance of a remarkable counterexample by Kaad and Skeide (J Operat Theory 89(2):343–348, 2023) we consider situations in which two Hilbert C*-modules <span>(M subset N)</span> with <span>(M^bot = { 0 })</span> over a fixed C*-algebra <i>A</i> of coefficients cannot be separated by a non-trivial bounded <i>A</i>-linear functional <span>(r_0: N rightarrow A)</span> vanishing on <i>M</i>. In other words, the uniqueness of extensions of the zero functional from <i>M</i> to <i>N</i> is focussed. We show this uniqueness of extension for any such pairs of Hilbert C*-modules over W*-algebras, over monotone complete C*-algebras and over compact C*-algebras. Moreover, uniqueness of extension takes place also for any one-sided maximal modular ideal of any C*-algebra. Such a non-zero separating bounded <i>A</i>-linear functional <span>(r_0)</span> exist for a given pair of full Hilbert C*-modules <span>(M subseteq N)</span> over a given C*-algebra <i>A</i> iff there exists a bounded <i>A</i>-linear non-adjointable operator <span>(T_0: N rightarrow N)</span>, such that the kernel of <span>(T_0)</span> is not biorthogonally closed w.r.t. <i>N</i> and contains <i>M</i>. This is a new perspective on properties of bounded modular operators that might appear in Hilbert C*-module theory. By the way, we find a correct proof of Lemma 2.4 of Frank (Int J Math 13:1–19, 2002) in the case of monotone complete and compact C*-algebras, but find it not valid in certain particular cases.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-024-00320-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139770202","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 creating new essential spectrum by self-adjoint extension of gapped operators 论通过间隙算子的自联合扩展创建新的基本谱
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-02-16 DOI: 10.1007/s43034-024-00319-y
Alessandro Michelangeli
{"title":"On creating new essential spectrum by self-adjoint extension of gapped operators","authors":"Alessandro Michelangeli","doi":"10.1007/s43034-024-00319-y","DOIUrl":"10.1007/s43034-024-00319-y","url":null,"abstract":"<div><p>Given a densely defined and gapped symmetric operator with infinite deficiency index, it is shown how self-adjoint extensions admitting arbitrarily prescribed portions of the gap as essential spectrum are identified and constructed within a general extension scheme. The emergence of new spectrum in the gap by self-adjoint extension is a problem with a long history and recent deep understanding, and yet it remains topical in several recent applications. Whereas it is already an established fact that, in case of infinite deficiency index, any kind of spectrum inside the gap can be generated by a suitable self-adjoint extension, the present discussion has the virtue of showing the clean and simple operator-theoretic mechanism of emergence of such extensions.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769889","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
Lipschitz continuity of the dilation of Bloch functions on the unit ball of a Hilbert space and applications 希尔伯特空间单位球上布洛赫函数扩张的 Lipschitz 连续性及其应用
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-02-13 DOI: 10.1007/s43034-024-00317-0
Alejandro Miralles
{"title":"Lipschitz continuity of the dilation of Bloch functions on the unit ball of a Hilbert space and applications","authors":"Alejandro Miralles","doi":"10.1007/s43034-024-00317-0","DOIUrl":"10.1007/s43034-024-00317-0","url":null,"abstract":"<div><p>Let <span>(B_E)</span> be the open unit ball of a complex finite- or infinite-dimensional Hilbert space. If <i>f</i> belongs to the space <span>(mathcal {B}(B_E))</span> of Bloch functions on <span>(B_E)</span>, we prove that the dilation map given by <span>(x mapsto (1-Vert xVert ^2) mathcal {R}f(x))</span> for <span>(x in B_E)</span>, where <span>(mathcal {R}f)</span> denotes the radial derivative of <i>f</i>, is Lipschitz continuous with respect to the pseudohyperbolic distance <span>(rho _E)</span> in <span>(B_E)</span>, which extends to the finite- and infinite-dimensional setting the result given for the classical Bloch space <span>(mathcal {B})</span>. To provide this result, we will need to prove that <span>(rho _E(zx,zy) le |z| rho _E(x,y))</span> for <span>(x,y in B_E)</span> under some conditions on <span>(z in mathbb {C})</span>. Lipschitz continuity of <span>(x mapsto (1-Vert xVert ^2) mathcal {R}f(x))</span> will yield some applications on interpolating sequences for <span>(mathcal {B}(B_E))</span> which also extends classical results from <span>(mathcal {B})</span> to <span>(mathcal {B}(B_E))</span>. Indeed, we show that it is necessary for a sequence in <span>(B_E)</span> to be separated to be interpolating for <span>(mathcal {B}(B_E))</span> and we also prove that any interpolating sequence for <span>(mathcal {B}(B_E))</span> can be slightly perturbed and it remains interpolating.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-024-00317-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139770003","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
Lorentz spaces depending on more than two parameters 取决于两个以上参数的洛伦兹空间
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-02-08 DOI: 10.1007/s43034-023-00313-w
Albrecht Pietsch
{"title":"Lorentz spaces depending on more than two parameters","authors":"Albrecht Pietsch","doi":"10.1007/s43034-023-00313-w","DOIUrl":"10.1007/s43034-023-00313-w","url":null,"abstract":"<div><p>For more than 50 years, the author has asked himself why Lorentz spaces are only defined for two parameters. Has this choice been made just for simplicity or is it a natural bound that cannot be exceeded? This question is <b>principal</b> and has nothing to do with <b>usefulness</b>. Now, I discovered a way to produce Lorentz sequence spaces for any finite number of parameters. Having found the right approach, everything turns out to be elementary; the presentation becomes an orgy of mathematical induction. Unfortunately, the new spaces are only of theoretical interest, since we do not know any handy description of their members. This dilemma is, most likely, the reason for the restriction to two, regretted above. However, by the axiom of choice, mathematicians are used to deals with objects that exist only formally; see Banach limits. Therefore, our situation is much more comfortable. It is recommended that, as a first step, readers should have a short glance at the last section, where historical aspects and the interplay between basic concepts are described. Apart from proved theorems, the paper contains many open problems. It is motivated by the same spirit as my very last bibitem in the references. Senior mathematicians should show the way into the future.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769777","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
Spectral enclosures for some unbounded (ntimes n) operator matrices 一些无约束 $$ntimes n$$ 算子矩阵的谱包围
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-01-31 DOI: 10.1007/s43034-024-00316-1
Yaru Qi, Yuying Li, Yihui Kong
{"title":"Spectral enclosures for some unbounded (ntimes n) operator matrices","authors":"Yaru Qi,&nbsp;Yuying Li,&nbsp;Yihui Kong","doi":"10.1007/s43034-024-00316-1","DOIUrl":"10.1007/s43034-024-00316-1","url":null,"abstract":"<div><p>In this paper, we establish the enclosures for the spectrum of unbounded <span>(ntimes n)</span> operator matrices in a Banach space. For diagonally dominant and off-diagonally dominant operator matrices, we present a new Gershgorin-type results on the localization of the spectrum by using the Schur complements and the quadratic complements, respectively, that no longer requires dominance order of 0 nor <span>(&lt;1)</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139644731","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
A note on commutator-simple algebras 关于换元简单代数的说明
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-01-25 DOI: 10.1007/s43034-023-00314-9
Jiankui Li, Shaoze Pan, Cangyuan Wang
{"title":"A note on commutator-simple algebras","authors":"Jiankui Li,&nbsp;Shaoze Pan,&nbsp;Cangyuan Wang","doi":"10.1007/s43034-023-00314-9","DOIUrl":"10.1007/s43034-023-00314-9","url":null,"abstract":"<div><p>We investigate the property of commutator-simplicity in algebras from both algebraic and analytic perspectives. We demonstrate that a large class of algebras possess this property. As an analytic analog, we introduce the concept of topological commutator-simplicity for Banach algebras and establish that a <span>(sigma )</span>-unital <span>(C^{*})</span>-algebra is topological commutator-simple if and only if its multiplier algebra is. Furthermore, we explore the applications of commutator-simplicity to certain equations involving commutators, emphasizing its relevance in the study of derivations. Specifically, we obtain that every continuous local derivation on <span>(L^1(G,omega ))</span> is a derivation when <i>G</i> is a unimodular locally compact group with a diagonal bounded weight <span>(omega )</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139554845","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
Lie derivable maps on nest algebras 巢状代数上的列可导映射
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-01-25 DOI: 10.1007/s43034-023-00315-8
Lei Liu, Kaipeng Li
{"title":"Lie derivable maps on nest algebras","authors":"Lei Liu,&nbsp;Kaipeng Li","doi":"10.1007/s43034-023-00315-8","DOIUrl":"10.1007/s43034-023-00315-8","url":null,"abstract":"<div><p>Let <span>(mathcal {N})</span> be a non-trivial nest on a Hilbert space <i>H</i> and <span>(textrm{alg}mathcal {N})</span> be the associated nest algebra. Let <span>(Gin textrm{alg}mathcal {N})</span> be an operator with <span>(overline{textrm{ran}(G)}in mathcal {N}backslash {H})</span>. In this note, we give a description of Lie derivable maps and generalized Lie 2-derivable maps at <i>G</i> of nest algebra <span>(textrm{alg}mathcal {N})</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139555043","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
Fredholm properties of a class of coupled operator matrices and their applications 一类耦合算子矩阵的弗雷德霍尔姆特性及其应用
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-01-18 DOI: 10.1007/s43034-024-00318-z
Jing Xu, Junjie Huang, Alatancang Chen
{"title":"Fredholm properties of a class of coupled operator matrices and their applications","authors":"Jing Xu,&nbsp;Junjie Huang,&nbsp;Alatancang Chen","doi":"10.1007/s43034-024-00318-z","DOIUrl":"10.1007/s43034-024-00318-z","url":null,"abstract":"<div><p>This paper deals with Fredholm properties of the one-sided coupled operator matrix <span>({mathcal {M}}=left( begin{array}{cc} A &amp;{} B 0 &amp;{} D end{array} right) left( begin{array}{cc} I &amp;{} 0 L &amp;{} I end{array} right))</span> by means of generalized Schur factorization and the associated space decompositions. For <span>(lambda in {mathbb {C}},)</span> some sufficient conditions are given for <span>(lambda -{mathcal {M}})</span> to be Fredholm (resp. left or right Fredholm), and these conclusions are further used to determine the essential spectra of a delay equation and a wave equation with acoustic boundary conditions.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139501464","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
Projective and injective tensor products of Banach (L^0)-modules 巴拿赫 $L^0$$ 模块的投影和注入张量积
IF 1 3区 数学
Annals of Functional Analysis Pub Date : 2024-01-08 DOI: 10.1007/s43034-023-00312-x
Enrico Pasqualetto
{"title":"Projective and injective tensor products of Banach (L^0)-modules","authors":"Enrico Pasqualetto","doi":"10.1007/s43034-023-00312-x","DOIUrl":"10.1007/s43034-023-00312-x","url":null,"abstract":"<div><p>We study projective and injective tensor products of Banach <span>(L^0)</span>-modules over a <span>(sigma )</span>-finite measure space. En route, we extend to Banach <span>(L^0)</span>-modules several technical tools of independent interest, such as quotient operators, summable families, and Schauder bases.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-023-00312-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139396577","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
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