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Some characterizations of minimal matrices with operator norm 具有算子规范的最小矩阵的一些特征
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-11-05 DOI: 10.1007/s43034-024-00393-2
Shuaijie Wang, Ying Zhang
{"title":"Some characterizations of minimal matrices with operator norm","authors":"Shuaijie Wang,&nbsp;Ying Zhang","doi":"10.1007/s43034-024-00393-2","DOIUrl":"10.1007/s43034-024-00393-2","url":null,"abstract":"<div><p>This paper studies matrices <i>A</i> in <span>(M_n(mathbb C))</span> satisfying </p><div><div><span>$$begin{aligned} Vert AVert =min {Vert A+BVert :Bin {mathcal {B}}}, end{aligned}$$</span></div></div><p>where <span>({mathcal {B}})</span> is a C*-subalgebra of <span>(M_n(mathbb C))</span> and <span>(Vert cdot Vert )</span> denotes the operator norm. Such an <i>A</i> is called <span>({mathcal {B}})</span>-minimal. The necessary and sufficient conditions for <i>A</i> to be <span>({mathcal {B}})</span>-minimal are characterized, and a constructive method to obtain <span>({mathcal {B}})</span>-minimal normal matrices is provided. Moreover, <span>(bigoplus _{i=1}^k{mathcal {B}})</span>-minimal normal matrices with anti-diagonal block form are studied.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142587710","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
Topological radicals, IX: relations in ideals of C*-algebras 拓扑自由基，IX：C* 矩阵理想中的关系
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-10-18 DOI: 10.1007/s43034-024-00391-4
Edward Kissin, Victor S. Shulman, Yurii V. Turovskii
{"title":"Topological radicals, IX: relations in ideals of C*-algebras","authors":"Edward Kissin,&nbsp;Victor S. Shulman,&nbsp;Yurii V. Turovskii","doi":"10.1007/s43034-024-00391-4","DOIUrl":"10.1007/s43034-024-00391-4","url":null,"abstract":"<div><p>In this paper, we pursue three aims. The first one is to apply Amitsur’s relations and radicals theory to the study of the lattices <span>(hbox {Id}_{{A}})</span> of closed two-sided ideals of C*-algebras <i>A</i>. We show that many new and many well-known results about C*-algebras follow naturally from this approach. To use “relation-radical” approach, we consider various subclasses of the class <span>({mathfrak {A}})</span> of all C*-algebras, which we call C*-properties, as they often linked to some properties of C*-algebras. We consider C*-properties <i>P</i> consisting of CCR- and of GCR-algebras; of C*-algebras with continuous trace; of real rank zero, AF, nuclear C*-algebras, etc. Each <i>P</i> defines reflexive relations <span>(ll _{{P}})</span> in all lattices <span>(hbox {Id}_{A}.)</span> Our second aim is to determine the hierarchy and interconnection between properties in <span>({mathfrak {A}}.)</span> Our third aim is to study the link between the radicals of relations <span>(ll _{{P}})</span> in the lattices <span>(hbox {Id}_{{A}})</span> and the topological radicals on <span>({mathfrak {A}}.)</span></p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142451107","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
Morita invariance of unbounded bivariant K-theory 无界双变量 K 理论的莫里塔不变性
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-10-01 DOI: 10.1007/s43034-024-00392-3
Jens Kaad
{"title":"Morita invariance of unbounded bivariant K-theory","authors":"Jens Kaad","doi":"10.1007/s43034-024-00392-3","DOIUrl":"10.1007/s43034-024-00392-3","url":null,"abstract":"<div><p>We introduce a notion of Morita equivalence for non-selfadjoint operator algebras equipped with a completely isometric involution (operator <span>(*)</span>-algebras). We then show that the unbounded Kasparov product by a Morita equivalence bimodule induces an isomorphism between equivalence classes of twisted spectral triples over Morita equivalent operator <span>(*)</span>-algebras. This leads to a tentative definition of unbounded bivariant <i>K</i>-theory and we prove that this bivariant theory is related to Kasparov’s bivariant <i>K</i>-theory via the Baaj-Julg bounded transform. Moreover, the unbounded Kasparov product provides a refinement of the usual interior Kasparov product. We illustrate our results by proving <span>(C^1)</span>-versions of well-known <span>(C^*)</span>-algebraic Morita equivalences in the context of hereditary subalgebras, conformal equivalences and crossed products by discrete groups.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43034-024-00392-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142409319","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
Zeta zeros and prolate wave operators 泽塔零点和凸面波算子
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-09-18 DOI: 10.1007/s43034-024-00388-z
Alain Connes, Caterina Consani, Henri Moscovici
{"title":"Zeta zeros and prolate wave operators","authors":"Alain Connes,&nbsp;Caterina Consani,&nbsp;Henri Moscovici","doi":"10.1007/s43034-024-00388-z","DOIUrl":"10.1007/s43034-024-00388-z","url":null,"abstract":"<div><p>We integrate in the framework of the semilocal trace formula two recent discoveries on the spectral realization of the zeros of the Riemann zeta function by introducing a semilocal analogue of the prolate wave operator. The latter plays a key role both in the spectral realization of the low lying zeros of zeta—using the positive part of its spectrum—and of their ultraviolet behavior—using the Sonin space which corresponds to the negative part of the spectrum. In the archimedean case the prolate operator is the sum of the square of the scaling operator with the grading of orthogonal polynomials, and we show that this formulation extends to the semilocal case. We prove the stability of the semilocal Sonin space under the increase of the finite set of places which govern the semilocal framework and describe their relation with Hilbert spaces of entire functions. Finally, we relate the prolate operator to the metaplectic representation of the double cover of <span>({text {SL}}(2,mathbb {R}))</span> with the goal of obtaining (in a forthcoming paper) a second candidate for the semilocal prolate operator.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254477","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 norm estimates for the triangular projection on the space of bounded linear operators between two symmetric sequence spaces 两个对称序列空间之间有界线性算子空间上三角投影的一些规范估计值
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-09-10 DOI: 10.1007/s43034-024-00385-2
Anna Tomskova
{"title":"Some norm estimates for the triangular projection on the space of bounded linear operators between two symmetric sequence spaces","authors":"Anna Tomskova","doi":"10.1007/s43034-024-00385-2","DOIUrl":"10.1007/s43034-024-00385-2","url":null,"abstract":"<div><p>For two given symmetric sequence spaces <i>E</i> and <i>F</i> we study the action of the main triangular projection <i>T</i> on <i>B</i>(<i>E</i>, <i>F</i>), the space of all bounded linear operators from <i>E</i> to <i>F</i>, and give a lower estimate for the norm of <i>T</i> in terms of the fundamental functions of <i>E</i> and <i>F</i> and the fundamental function of the generalized dual space <i>F</i> : <i>E</i>. In addition, we give a condition for the boundedness of the operator <i>T</i> in terms of <i>F</i>-absolutely summing operators. Furthermore, we apply our results to some concrete symmetric sequence spaces. In particular, we study the question of the boundedness or unboundedness of <i>T</i> on the spaces <span>(B(ell _{p_1,q_1},ell _{p}),)</span> <span>(B(ell _{p},ell _{p_1,q_1}))</span> and <span>(B(ell _{p_1,q_1},ell _{p_2,q_2}))</span>.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210777","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
Interpolatory quincunx quasi-tight and tight framelets 互推五边形准紧密和紧密小方格
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-09-06 DOI: 10.1007/s43034-024-00390-5
Ran Lu
{"title":"Interpolatory quincunx quasi-tight and tight framelets","authors":"Ran Lu","doi":"10.1007/s43034-024-00390-5","DOIUrl":"10.1007/s43034-024-00390-5","url":null,"abstract":"<div><p>Constructing multivariate tight framelets is a challenging problem in wavelet and framelet theory. The problem is intrinsically related to the Hermitian sum of squares decomposition of multivariate trigonometric polynomials and the spectral factorization of multivariate trigonometric polynomial matrices. To circumvent the relevant difficulties, the notion of a quasi-tight framelet has been introduced in recent years, which generalizes the concept of tight framelets. On one hand, quasi-tight framelets behave similarly to tight framelets. On the other hand, compared to tight framelets, quasi-tight framelets have much more flexibility and advantages. Motivated by several recent studies of multivariate quasi-tight and tight framelets, we work on quincunx quasi-tight and tight framelets with the interpolatory properties in this paper. We first show that from any interpolatory quincunx refinement filter, one can always construct an interpolatory quasi-tight framelet with three generators. Next, we shall present a way to construct interpolatory quincunx quasi-tight framelets with high-order vanishing moments. Finally, we will establish an algorithm to construct interpolatory quincunx tight framelets from any interpolatory quincunx refinement filter that satisfies the so-called sum-of-squares (SOS) condition. All our proofs are constructive, and several examples in dimension <span>(d=2)</span> will be provided to illustrate our main results.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210778","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 sharp bounds for Hardy-type operators on mixed radial-angular type function spaces 混合径向角型函数空间上哈代型算子的若干尖锐边界
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-09-04 DOI: 10.1007/s43034-024-00389-y
Ronghui Liu, Yanqi Yang, Shuangping Tao
{"title":"Some sharp bounds for Hardy-type operators on mixed radial-angular type function spaces","authors":"Ronghui Liu,&nbsp;Yanqi Yang,&nbsp;Shuangping Tao","doi":"10.1007/s43034-024-00389-y","DOIUrl":"10.1007/s43034-024-00389-y","url":null,"abstract":"<div><p>In this paper, we are devoted to studying some sharp bounds for Hardy-type operators on mixed radial-angular type function spaces. In addition, we will establish the sharp weak-type estimates for the fractional Hardy operator and its conjugate operator, respectively.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210794","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 spectral eigenmatrix problem for the planar self-affine measures with three digits 关于三位数平面自参量的谱特征矩阵问题
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-08-27 DOI: 10.1007/s43034-024-00386-1
Jing-Cheng Liu, Ming Liu, Min-Wei Tang, Sha Wu
{"title":"On spectral eigenmatrix problem for the planar self-affine measures with three digits","authors":"Jing-Cheng Liu,&nbsp;Ming Liu,&nbsp;Min-Wei Tang,&nbsp;Sha Wu","doi":"10.1007/s43034-024-00386-1","DOIUrl":"10.1007/s43034-024-00386-1","url":null,"abstract":"<div><p>Let <span>(mu _{M,D})</span> be a self-affine measure generated by an iterated function systems <span>({phi _d(x)=M^{-1}(x+d) (xin mathbb {R}^2)}_{din D})</span>, where <span>(Min M_2(mathbb {Z}))</span> is an expanding integer matrix and <span>(D = {(0,0)^t,(1,0)^t,(0,1)^t})</span>. In this paper, we study the spectral eigenmatrix problem of <span>(mu _{M,D})</span>, i.e., we characterize the matrix <i>R</i> which <span>(RLambda )</span> is also a spectrum of <span>(mu _{M,D})</span> for some spectrum <span>(Lambda )</span>. Some necessary and sufficient conditions for <i>R</i> to be a spectral eigenmatrix are given, which extends some results of An et al. (Indiana Univ Math J, 7(1): 913–952, 2022). Moreover, we also find some irrational spectral eigenmatrices of <span>(mu _{M,D})</span>, which is different from the known results that spectral eigenmatrices are rational.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226727","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
Toeplitz operators and group-moment coordinates for quasi-elliptic and quasi-hyperbolic symbols 准椭圆和准双曲符号的托普利兹算子和群矩坐标
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-08-26 DOI: 10.1007/s43034-024-00387-0
Raúl Quiroga-Barranco, Armando Sánchez-Nungaray
{"title":"Toeplitz operators and group-moment coordinates for quasi-elliptic and quasi-hyperbolic symbols","authors":"Raúl Quiroga-Barranco,&nbsp;Armando Sánchez-Nungaray","doi":"10.1007/s43034-024-00387-0","DOIUrl":"10.1007/s43034-024-00387-0","url":null,"abstract":"<div><p>For <span>(mathbb {B}^n)</span> the <i>n</i>-dimensional unit ball and <span>(D_n)</span> its Siegel unbounded realization, we consider Toeplitz operators acting on weighted Bergman spaces with symbols invariant under the actions of the maximal Abelian subgroups of biholomorphisms <span>(mathbb {T}^n)</span> (quasi-elliptic) and <span>(mathbb {T}^n times mathbb {R}_+)</span> (quasi-hyperbolic). Using geometric symplectic tools (Hamiltonian actions and moment maps) we obtain simple diagonalizing spectral integral formulas for such kinds of operators. Some consequences show how powerful the use of our differential geometric methods are.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210779","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
Decomposition of the set of Banach limits into discrete and continuous subsets 将巴拿赫极限集合分解为离散和连续子集
IF 1.2 3区 数学
Annals of Functional Analysis Pub Date : 2024-08-16 DOI: 10.1007/s43034-024-00382-5
Nikolai Avdeev, Evgenii Semenov, Alexandr Usachev, Roman Zvolinskii
{"title":"Decomposition of the set of Banach limits into discrete and continuous subsets","authors":"Nikolai Avdeev,&nbsp;Evgenii Semenov,&nbsp;Alexandr Usachev,&nbsp;Roman Zvolinskii","doi":"10.1007/s43034-024-00382-5","DOIUrl":"10.1007/s43034-024-00382-5","url":null,"abstract":"<div><p>The aim of this work is to describe subsets of Banach limits in terms of a certain functional characteristic. We compute radii and cardinalities for some of these subsets.</p></div>","PeriodicalId":48858,"journal":{"name":"Annals of Functional Analysis","volume":null,"pages":null},"PeriodicalIF":1.2,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142210780","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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