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Annals of Functional Analysis最新文献

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Application of Banach limits to invariant measures of infinite-dimensional Hamiltonian flows 巴拿赫极限在无穷维哈密顿流不变度量中的应用
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-03-21 DOI: 10.1007/s43034-024-00332-1
V. Zh. Sakbaev
{"title":"Application of Banach limits to invariant measures of infinite-dimensional Hamiltonian flows","authors":"V. Zh. Sakbaev","doi":"10.1007/s43034-024-00332-1","DOIUrl":"10.1007/s43034-024-00332-1","url":null,"abstract":"<div><p>Applying an invariant measure on phase space, we study the Koopman representation of a group of symplectomorphisms in an infinite-dimensional Hilbert space equipped with a translation-invariant symplectic form. The phase space is equipped with a finitely additive measure, invariant under the group of symplectomorphisms generated by Liouville-integrable Hamiltonian systems. We construct an invariant measure of Lebesgue type by applying a special countable product of Lebesgue measures on real lines. An invariant measure of Banach type is constructed by applying a countable product of Banach measures (defined by the Banach limit) on real lines. One of the advantages of an invariant measure of Banach type compared to an invariant measure of Lebesgue type is finiteness of the values of this measure in the entire space. The introduced invariant measures help us to describe both the strong continuity subspaces of the Koopman unitary representation of an infinite-dimensional Hamiltonian flow and the spectral properties of the constraint generator of the unitary representation on the invariant strong continuity subspace.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140199063","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
M-serially summing operators on Banach lattices 巴拿赫网格上的 M 序列求和算子
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-03-16 DOI: 10.1007/s43034-024-00331-2
Fu Zhang, Hanhan Shen, Zili Chen
{"title":"M-serially summing operators on Banach lattices","authors":"Fu Zhang,&nbsp;Hanhan Shen,&nbsp;Zili Chen","doi":"10.1007/s43034-024-00331-2","DOIUrl":"10.1007/s43034-024-00331-2","url":null,"abstract":"<div><p>Let <i>E</i>, <i>F</i> be Banach lattices, where <i>E</i> has the disjoint Riesz decomposition property. For a lattice homomorphism <span>(T:Erightarrow F)</span> and a bounded subset <i>A</i> of <i>E</i>, we establish a necessary and sufficient condition under which <i>TA</i> is <i>b</i>-order bounded. Based on this, we study the <i>b</i>-order boundedness of subsets of <i>E</i> and obtain several characterizations of <i>AM</i>-spaces. Furthermore, we introduce and investigate a novel type of operators referred to as <i>M</i>-serially summing operator. The connections of this category of operators with classical notions of operators, such as majorizing operators, preregular operators and serially summing operators, are considered.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140147232","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
Disjoint subspace-hypercyclic operators on separable Banach spaces 可分离巴拿赫空间上的不相交子空间超循环算子
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-03-14 DOI: 10.1007/s43034-024-00322-3
Renyu Chen, Xiang Chen, Zehua Zhou
{"title":"Disjoint subspace-hypercyclic operators on separable Banach spaces","authors":"Renyu Chen,&nbsp;Xiang Chen,&nbsp;Zehua Zhou","doi":"10.1007/s43034-024-00322-3","DOIUrl":"10.1007/s43034-024-00322-3","url":null,"abstract":"<div><p>In this paper, we initially introduce the concept of disjoint subspace-hypercyclic operators and illustrate that disjoint subspace-hypercyclic operators differ from disjoint hypercyclic operators. Furthermore, we obtain two different criteria for disjoint subspace-hypercyclic operators. Finally, we discover an equivalent condition regarding the bilateral forward weighted shift operators’ disjoint subspace-transitivity on <span>(c_{0}(mathbb {Z}))</span> or <span>(l^{p}(mathbb {Z}))</span> in a certain special case.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140129040","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
Block dual Toeplitz operators on the orthogonal complement of the Dirichlet space 迪里希勒空间正交补集上的整块对偶托普利兹算子
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-03-11 DOI: 10.1007/s43034-024-00329-w
Chunxu Xu, Jianxiang Dong, Tao Yu
{"title":"Block dual Toeplitz operators on the orthogonal complement of the Dirichlet space","authors":"Chunxu Xu,&nbsp;Jianxiang Dong,&nbsp;Tao Yu","doi":"10.1007/s43034-024-00329-w","DOIUrl":"10.1007/s43034-024-00329-w","url":null,"abstract":"<div><p>We give some characterizations of block dual Toeplitz operators acting on the orthogonal complement of the Dirichlet space. We characterized the compactness of the finite sum of block dual Toeplitz products. Commuting block dual Toeplitz operators and quasinormal block dual Toeplitz operators are also considered.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140129123","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
Some new weighted weak-type iterated and bilinear modified Hardy inequalities 一些新的加权弱型迭代和双线性修正哈代不等式
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-03-02 DOI: 10.1007/s43034-024-00327-y
V. García García, P. Ortega Salvador
{"title":"Some new weighted weak-type iterated and bilinear modified Hardy inequalities","authors":"V. García García,&nbsp;P. Ortega Salvador","doi":"10.1007/s43034-024-00327-y","DOIUrl":"10.1007/s43034-024-00327-y","url":null,"abstract":"<div><p>We characterize the good weights for some weighted weak-type iterated and bilinear modified Hardy inequalities to hold.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-024-00327-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140019097","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
Common properties of a and b satisfying (ab^n = b^{n+1}) and (ba^n = a^{n+1}) in Banach algebras 巴拿赫代数中满足 $ab^n = b^{n+1}$$ 和 $ba^n = a^{n+1}$$ 的 a 和 b 的共同性质
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-02-27 DOI: 10.1007/s43034-024-00328-x
Fei Peng, Xiaoxiang Zhang
{"title":"Common properties of a and b satisfying (ab^n = b^{n+1}) and (ba^n = a^{n+1}) in Banach algebras","authors":"Fei Peng,&nbsp;Xiaoxiang Zhang","doi":"10.1007/s43034-024-00328-x","DOIUrl":"10.1007/s43034-024-00328-x","url":null,"abstract":"<div><p>This paper describes the common properties of elements <i>a</i> and <i>b</i> satisfying <span>(ab^n = b^{n + 1})</span> and <span>(ba^n = a^{n + 1})</span> in the settings of Banach algebras, rings and operator algebras from the viewpoint of generalized inverses and spectral theory, where <i>n</i> is a positive integer. As applications, we show that if </p><div><div><span>$$begin{aligned} M_0 = begin{pmatrix} T &amp;{} 0 0 &amp;{} N_0 end{pmatrix}, M_1 = begin{pmatrix} T &amp;{} S 0 &amp;{} N_1 end{pmatrix} text {and} M_2 = begin{pmatrix} T &amp;{} 0 W &amp;{} N_2 end{pmatrix} end{aligned}$$</span></div></div><p>are triangular operator matrices acting on the Banach space <span>(X oplus X)</span> such that <span>(N_0, N_1)</span> and <span>(N_2)</span> are nilpotent, then many subsets of the spectrum of <span>(M_0)</span> are the same with those of <span>(M_1)</span> and <span>(M_2.)</span> Moreover, we improve some recent extensions of Jacobson’s lemma and Cline’s formula for the Drazin inverse, generalized Drazin inverse and generalized Drazin–Riesz inverse.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140010082","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
Two weight estimates for (L^{r})-Hörmander singular integral operators and rough singular integral operators with matrix weights 带矩阵权重的 $$L^{r}$$ - 赫尔曼德奇异积分算子和粗糙奇异积分算子的两个权重估计值
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-02-27 DOI: 10.1007/s43034-024-00326-z
Yongming Wen, Wenting Hu, Fuli Ku
{"title":"Two weight estimates for (L^{r})-Hörmander singular integral operators and rough singular integral operators with matrix weights","authors":"Yongming Wen,&nbsp;Wenting Hu,&nbsp;Fuli Ku","doi":"10.1007/s43034-024-00326-z","DOIUrl":"10.1007/s43034-024-00326-z","url":null,"abstract":"<div><p>In this paper, we give new bump conditions for two matrix weight inequalities of <span>(L^{r})</span>-Hörmander singular integral operators and rough singular integral operators, which are new even in the scalar cases. As applications, we obtain quantitative one weight inequalities for rough singular integral operators.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140010083","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
Making more approximate oblique dual frame pairs 制作更多近似斜双框对
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-02-25 DOI: 10.1007/s43034-024-00325-0
Yun-Zhang Li, Li-Juan Wu
{"title":"Making more approximate oblique dual frame pairs","authors":"Yun-Zhang Li,&nbsp;Li-Juan Wu","doi":"10.1007/s43034-024-00325-0","DOIUrl":"10.1007/s43034-024-00325-0","url":null,"abstract":"<div><p>The concept of approximate oblique dual frame was introduced by Díaz, Heineken and Morillas. It is more general than traditional dual frame, oblique dual frame, and approximate dual frame. This paper addresses constructing more approximate oblique dual frame pairs starting from one given oblique dual frame pair. Using “analysis and synthesis operator”, “portrait”, and “gap” perturbation techniques, we present several sufficient conditions for constructing approximate oblique dual frame pairs under the general Hilbert space setting. As an application, we then focus on constructing approximate oblique dual frame pairs in shift-invariant subspaces of <span>(L^{2}(mathbb R))</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139969146","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
Composition operators on weighted Fock spaces induced by (A_{infty })-type weights 由 $$A_{infty }$ 类权重诱导的加权 Fock 空间上的合成算子
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-02-23 DOI: 10.1007/s43034-024-00324-1
Jiale Chen
{"title":"Composition operators on weighted Fock spaces induced by (A_{infty })-type weights","authors":"Jiale Chen","doi":"10.1007/s43034-024-00324-1","DOIUrl":"10.1007/s43034-024-00324-1","url":null,"abstract":"<div><p>In this paper, we study the composition operators <span>(C_{varphi })</span> acting on the weighted Fock spaces <span>(F^p_{alpha ,w})</span>, where <i>w</i> is a weight satisfying some restricted <span>(A_{infty })</span>-conditions. We first characterize the boundedness and compactness of the composition operators <span>(C_{varphi }:F^p_{alpha ,w}rightarrow F^q_{beta ,v})</span> for all <span>(0&lt;p,q&lt;infty)</span> in terms of certain Berezin type integral transforms. A new condition for the bounded embedding <span>(I_d:F^p_{alpha ,w}rightarrow L^q(mathbb {C},mu ))</span> in the case <span>(p&gt;q)</span> is also obtained. Then, in the case that <span>(w(z)=(1+|z|)^{mp})</span> for <span>(min mathbb {R})</span>, using some Taylor coefficient estimates, we establish an upper bound for the approximation numbers of composition operators acting on <span>(F^p_{alpha ,w})</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139953062","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
p-Compactness of Bloch maps 布洛赫映射的 p-紧密性
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-02-21 DOI: 10.1007/s43034-024-00321-4
A. Jiménez-Vargas, D. Ruiz-Casternado
{"title":"p-Compactness of Bloch maps","authors":"A. Jiménez-Vargas,&nbsp;D. Ruiz-Casternado","doi":"10.1007/s43034-024-00321-4","DOIUrl":"10.1007/s43034-024-00321-4","url":null,"abstract":"<div><p>Influenced by the concept of a <i>p</i>-compact operator due to Sinha and Karn (Stud Math 150(1): 17–33, 2002), we introduce <i>p</i>-compact Bloch maps of the open unit disk <span>(mathbb {D}subseteq mathbb {C})</span> to a complex Banach space <i>X</i>, and obtain its most outstanding properties: surjective Banach ideal property, Möbius invariance, linearisation on the Bloch-free Banach space over <span>(mathbb {D})</span>, inclusion properties, factorisation of their derivatives, and transposition on the normalized Bloch space. We also present right <i>p</i>-nuclear Bloch maps of <span>(mathbb {D})</span> to <i>X</i> and study its relation with <i>p</i>-compact Bloch maps.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-024-00321-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139925084","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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