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New s-number classes and summing classes of bilinear operators 双线性算子的新s数类和和类
IF 1 3区 数学
Annals of Functional Analysis Pub Date : 2025-08-20 DOI: 10.1007/s43034-025-00464-y
Eduardo Brandani da Silva, Dicesar Lass Fernandez
{"title":"New s-number classes and summing classes of bilinear operators","authors":"Eduardo Brandani da Silva,&nbsp;Dicesar Lass Fernandez","doi":"10.1007/s43034-025-00464-y","DOIUrl":"10.1007/s43034-025-00464-y","url":null,"abstract":"<div><p>We introduce classes of bilinear operators of <span>(ell _{p,q})</span>-type, i.e. classes of operators in which their sequences of s-numbers are in <span>(ell _{p,q},)</span> and their properties and relationships are studied. We also introduce two classes of summing bilinear operators: the class <span>(Pi _{p,q;r}^{ss})</span> of strongly summing operators, and the class <span>(Pi _{p,q;r,s}^{as})</span> of absolutely summing operators. These classes share some properties with similar proofs. But, some others properties are specific for one or the other class. Also, they are somewhat more general than the multilinear summing classes introduced before by several authors. Relationships between classes of <span>(ell _{p,q})</span>-type and summing classes are given.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144868910","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
Min–max relations for tuples of operators in terms of component spaces 在分量空间中算子元组的最小-最大关系
IF 1 3区 数学
Annals of Functional Analysis Pub Date : 2025-08-20 DOI: 10.1007/s43034-025-00465-x
Arpita Mal
{"title":"Min–max relations for tuples of operators in terms of component spaces","authors":"Arpita Mal","doi":"10.1007/s43034-025-00465-x","DOIUrl":"10.1007/s43034-025-00465-x","url":null,"abstract":"<div><p>For tuples of compact operators <span>(mathcal {T}=(T_1,ldots , T_d))</span> and <span>(mathcal {S}=(S_1,ldots ,S_d))</span> on Banach spaces over a field <span>(mathbb {F})</span>, considering the joint <i>p</i>-operator norms on the tuples, we study <span>(dist(mathcal {T},mathbb {F}^dmathcal {S}),)</span> the distance of <span>(mathcal {T})</span> from the <i>d</i>-dimensional subspace <span>(mathcal {F}^dmathcal {S}:={{textbf {z}}mathcal {S}:{textbf {z}}in mathbb {F}^d}.)</span> We obtain a relation between <span>(dist(mathcal {T},mathbb {F}^dmathcal {S}))</span> and <span>(dist(T_i,mathbb {F}S_i),)</span> for <span>(1le ile d.)</span> We prove that if <span>(p=infty ,)</span> then <span>(dist(mathcal {T},mathbb {F}^dmathcal {S})=underset{1le ile d}{max }dist(T_i,mathbb {F}S_i),)</span> and for <span>(1le p&lt;infty ,)</span> under a sufficient condition, <span>(dist(mathcal {T},mathbb {F}^dmathcal {S})^p=underset{1le ile d}{sum }dist(T_i,mathbb {F}S_i)^p.)</span> As a consequence, we deduce the equivalence of Birkhoff-James orthogonality, <span>(mathcal {T}perp _B mathbb {F}^dmathcal {S} Leftrightarrow T_iperp _B S_i,)</span> under a sufficient condition. Furthermore, we explore the relation of one sided Gâteaux derivatives of <span>(mathcal {T})</span> in the direction of <span>(mathcal {S})</span> with that of <span>(T_i)</span> in the direction of <span>(S_i.)</span> Applying this, we explore the relation between the smoothness of <span>(mathcal {T})</span> and <span>(T_i.)</span> By identifying an operator, whose range is <span>(ell _infty ^d,)</span> as a tuple of functionals, we effectively use the results obtained here for operators whose range is <span>(ell _infty ^d)</span> and deduce nice results involving functionals.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144880999","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
Locally unital (C^*)-algebras do not admit frames 局部一元(C^*) -代数不允许帧
IF 1 3区 数学
Annals of Functional Analysis Pub Date : 2025-08-18 DOI: 10.1007/s43034-025-00459-9
D. V. Fufaev
{"title":"Locally unital (C^*)-algebras do not admit frames","authors":"D. V. Fufaev","doi":"10.1007/s43034-025-00459-9","DOIUrl":"10.1007/s43034-025-00459-9","url":null,"abstract":"<div><p>We study non-unital <span>(C^*)</span>-algebras such that for any element, there exists a local unit and prove that in such algebras there are no frames. This fact was previously known only for commutative algebras. Among other results, we establish some necessary properties of frames in <span>(C^*)</span>-algebras (which are of independent interest in the noncommutative topology), and consider several examples of <span>(C^*)</span>-algebras that are new in this context.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144868929","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
Weak factorizations for Hardy spaces in the Dunkl setting Dunkl环境下Hardy空间的弱分解
IF 1 3区 数学
Annals of Functional Analysis Pub Date : 2025-08-11 DOI: 10.1007/s43034-025-00461-1
Qingdong Guo, Wenting Hu
{"title":"Weak factorizations for Hardy spaces in the Dunkl setting","authors":"Qingdong Guo,&nbsp;Wenting Hu","doi":"10.1007/s43034-025-00461-1","DOIUrl":"10.1007/s43034-025-00461-1","url":null,"abstract":"<div><p>In this paper, we establish the weak factorizations of the Hardy space associated with the Dunkl operator via the bilinear forms of Dunkl–Riesz transforms <span>({{mathcal {R}}_{j}}_{j=1}^{d}.)</span> Note that the kernels of <span>({{mathcal {R}}_{j}}_{j=1}^{d})</span> involve both the Euclidean and the Dunkl metrics, which are not equivalent. As an application, we provide a new proof for the sufficiency of characterization of the <span>({textrm{BMO}})</span> space associated to the Dunkl operator via the commutators of <span>({{mathcal {R}}_{j}}_{j=1}^{d}.)</span></p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144810850","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
Resolvent set analysis of the Bergman shift 伯格曼位移的解算集分析
IF 1 3区 数学
Annals of Functional Analysis Pub Date : 2025-08-09 DOI: 10.1007/s43034-025-00462-0
Wei He, Guoliang Zhu
{"title":"Resolvent set analysis of the Bergman shift","authors":"Wei He,&nbsp;Guoliang Zhu","doi":"10.1007/s43034-025-00462-0","DOIUrl":"10.1007/s43034-025-00462-0","url":null,"abstract":"<div><p>This paper studies the invariant subspaces of the Bergman shift using the resolvent set analysis approach introduced by Douglas and Yang. We construct invariants on the resolvent set of the Bergman shift to describe the Bergman inner functions and the inclusion relationship of invariant subspaces of the Bergman shift. We generalize the concept of power sets, originally introduced by Douglas and Yang for quasinilpotent operators, to any boundary point of the spectrum of any operator. We compute the newly defined power sets for the conjugate of a class of compression operators of the Bergman shift, and demonstrate how they reflect the structure of invariant subspaces.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163178","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
Weak nondensifiability in Banach spaces Banach空间中的弱非致密性
IF 1 3区 数学
Annals of Functional Analysis Pub Date : 2025-08-04 DOI: 10.1007/s43034-025-00456-y
Gonzalo García, Gaspar Mora
{"title":"Weak nondensifiability in Banach spaces","authors":"Gonzalo García,&nbsp;Gaspar Mora","doi":"10.1007/s43034-025-00456-y","DOIUrl":"10.1007/s43034-025-00456-y","url":null,"abstract":"<div><p>In the present paper, the notion of weak degree of nondensifiability, <i>w</i>-DND, is introduced. Likewise, we analyze its main properties, and we also prove that the <i>w</i>-DND is actually an upper bound for any measure of weak noncompactness. Moreover, for the De Blasi measure of weak noncompactness, such an upper bound is sharp. As an application of our results, we characterize both Schur and Dunford–Pettis properties of a Banach space in terms of the <i>w</i>-DND, which turns out this new concept into a useful tool in functional analysis.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161471","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 preduals of Banach space valued Bourgain–Morrey spaces Banach空间的前似值Bourgain-Morrey空间
IF 1 3区 数学
Annals of Functional Analysis Pub Date : 2025-08-04 DOI: 10.1007/s43034-025-00458-w
Tengfei Bai, Pengfei Guo, Jingshi Xu
{"title":"The preduals of Banach space valued Bourgain–Morrey spaces","authors":"Tengfei Bai,&nbsp;Pengfei Guo,&nbsp;Jingshi Xu","doi":"10.1007/s43034-025-00458-w","DOIUrl":"10.1007/s43034-025-00458-w","url":null,"abstract":"<div><p>Let <i>X</i> be a Banach space such that there exists a Banach space <span>(^*X)</span> satisfying <span>(( ^*X )^ *= X)</span>. In this paper, we introduce <i>X</i>-valued Bourgain–Morrey spaces. We show that <span>(^*X)</span>-valued block spaces are the predual of <i>X</i>-valued Bourgain–Morrey spaces. We obtain the completeness, denseness, and Fatou property of <span>(^*X)</span>-valued block spaces. We give a description of the dual of <i>X</i>-valued Bourgain–Morrey spaces and conclude the reflexivity of these spaces. The boundedness of powered Hardy–Littlewood maximal operator in vector-valued block spaces is obtained.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161470","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
An algebraic characterization of linearity for additive maps preserving orthogonality 保留正交性的加性映射线性的代数表征
IF 1 3区 数学
Annals of Functional Analysis Pub Date : 2025-08-01 DOI: 10.1007/s43034-025-00454-0
Lei Li, Siyu Liu, Antonio M. Peralta
{"title":"An algebraic characterization of linearity for additive maps preserving orthogonality","authors":"Lei Li,&nbsp;Siyu Liu,&nbsp;Antonio M. Peralta","doi":"10.1007/s43034-025-00454-0","DOIUrl":"10.1007/s43034-025-00454-0","url":null,"abstract":"<div><p>We study when an additive mapping preserving orthogonality between two complex inner product spaces is automatically complex-linear or conjugate-linear. Concretely, let <i>H</i> and <i>K</i> be complex inner product spaces with <span>(hbox{dim}(H)ge 2)</span>, and let <span>(A: Hrightarrow K)</span> be an additive map preserving orthogonality. We obtain that <i>A</i> is zero or a positive scalar multiple of a real-linear isometry from <i>H</i> into <i>K</i>. We further prove that the following statements are equivalent: </p><dl><dt><dfn>(a):</dfn></dt><dd>\u0000 <p><i>A</i> is complex-linear or conjugate-linear.</p>\u0000 </dd><dt><dfn>(b):</dfn></dt><dd>\u0000 <p>For every <span>(zin H)</span> we have <span>(A(i z) in {pm i A(z)})</span>.</p>\u0000 </dd><dt><dfn>(c):</dfn></dt><dd>\u0000 <p>There exists a non-zero point <span>(zin H)</span> such that <span>(A(i z) in {pm i A(z)})</span>.</p>\u0000 </dd><dt><dfn>(d):</dfn></dt><dd>\u0000 <p>There exists a non-zero point <span>(zin H)</span> such that <span>(i A(z) in A(H))</span>.</p>\u0000 </dd></dl><p>The mapping <i>A</i> is neither complex-linear nor conjugate-linear if, and only if, there exists a non-zero <span>(xin H)</span> such that <span>(i A(x)notin A(H))</span> (equivalently, for every non-zero <span>(xin H)</span>, <span>(i A(x)notin A(H))</span>). Among the consequences, we show that, under the hypothesis above, the mapping <i>A</i> is automatically complex-linear or conjugate-linear if <i>A</i> has dense range, or if <i>H</i> and <i>K</i> are finite dimensional with <span>(hbox{dim}(K)&lt; 2hbox{dim}(H))</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-025-00454-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145154131","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
Some geometric properties of spaces of vector-valued integrable functions 向量值可积函数空间的一些几何性质
IF 1 3区 数学
Annals of Functional Analysis Pub Date : 2025-07-25 DOI: 10.1007/s43034-025-00452-2
Mohit, Ranjana Jain
{"title":"Some geometric properties of spaces of vector-valued integrable functions","authors":"Mohit,&nbsp;Ranjana Jain","doi":"10.1007/s43034-025-00452-2","DOIUrl":"10.1007/s43034-025-00452-2","url":null,"abstract":"<div><p>We identify the smooth points of <span>(L^1(mu ,X))</span>, and provide some necessary and sufficient conditions for left and right symmetry of points with respect to Birkhoff–James orthogonality in <span>(L^p(mu ,X), 1le p&lt;infty)</span>, where <span>(mu)</span> is any complete positive measure and <i>X</i> is a Banach space with some suitable properties.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169352","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
On roots of normal operators and extensions of Ando’s Theorem 正规算子的根与安藤定理的推广
IF 1 3区 数学
Annals of Functional Analysis Pub Date : 2025-07-22 DOI: 10.1007/s43034-025-00455-z
Hranislav Stanković, Carlos Kubrusly
{"title":"On roots of normal operators and extensions of Ando’s Theorem","authors":"Hranislav Stanković,&nbsp;Carlos Kubrusly","doi":"10.1007/s43034-025-00455-z","DOIUrl":"10.1007/s43034-025-00455-z","url":null,"abstract":"<div><p>In this paper, we extend Ando’s theorem on paranormal operators, which states that if <span>(T in mathfrak {B}(mathcal {H}))</span> is a paranormal operator and there exists <span>(n in mathbb {N})</span> such that <span>(T^n)</span> is normal, then <span>(T)</span> is normal. We generalize this result to the broader classes of <span>(k)</span>-paranormal operators and absolute-<span>(k)</span>-paranormal operators. Furthermore, in the case of a separable Hilbert space <span>(mathcal {H})</span>, we show that if <span>(T in mathfrak {B}(mathcal {H}))</span> is a <span>(k)</span>-quasi-paranormal operator for some <span>(k in mathbb {N})</span>, and there exists <span>(n in mathbb {N})</span> such that <span>(T^n)</span> is normal, then <span>(T)</span> decomposes as <span>(T = T' oplus T'')</span>, where <span>(T')</span> is normal and <span>(T'')</span> is nilpotent of nil-index at most <span>(min {n,k+1})</span>, with either summand potentially absent.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":"16 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168540","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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