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Advances in Operator Theory最新文献

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Weighted Karcher means on unipotent Lie groups 单能李群上的加权卡彻手段
IF 0.8
Advances in Operator Theory Pub Date : 2024-03-21 DOI: 10.1007/s43036-024-00326-9
Jimmie Lawson
{"title":"Weighted Karcher means on unipotent Lie groups","authors":"Jimmie Lawson","doi":"10.1007/s43036-024-00326-9","DOIUrl":"10.1007/s43036-024-00326-9","url":null,"abstract":"<div><p>A substantial theory of the Karcher mean exists in the settings of Riemannian manifolds and positive matrix and operator spaces. Here a general setting for the study of the Karcher mean on Lie groups is proposed. Local existence and uniqueness results already exist, but here, a significant global result is obtained. It is shown that a natural computable iteration scheme for the Karcher mean exists for the Lie group of upper triangular unipotent matrices and that it always converges starting from any point after finitely many steps.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140222124","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Strong law of large numbers for double sequences of pairwise M-dependent real and multivalued random variables 依赖 M 的成对实数和多值随机变量双序列的强大数定律
IF 0.8
Advances in Operator Theory Pub Date : 2024-03-20 DOI: 10.1007/s43036-024-00318-9
El-Moustafid Mohamed, M’hamed El-Louh, Fatima Ezzaki
{"title":"Strong law of large numbers for double sequences of pairwise M-dependent real and multivalued random variables","authors":"El-Moustafid Mohamed,&nbsp;M’hamed El-Louh,&nbsp;Fatima Ezzaki","doi":"10.1007/s43036-024-00318-9","DOIUrl":"10.1007/s43036-024-00318-9","url":null,"abstract":"<div><p>The strong law of large numbers for a double sequence of pairwise <i>M</i>-dependent random variables is established. An extension to Kuratowski-convergence of the strong law of large numbers for a double sequence of pairwise <i>M</i>-dependent multivalued random variables with closed values is stated.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140226128","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The impact of a singular first-order term in some degenerate elliptic equations involving Hardy potential 涉及哈代势能的某些退化椭圆方程中奇异一阶项的影响
IF 0.8
Advances in Operator Theory Pub Date : 2024-03-14 DOI: 10.1007/s43036-024-00324-x
Hocine Ayadi, Rezak Souilah
{"title":"The impact of a singular first-order term in some degenerate elliptic equations involving Hardy potential","authors":"Hocine Ayadi,&nbsp;Rezak Souilah","doi":"10.1007/s43036-024-00324-x","DOIUrl":"10.1007/s43036-024-00324-x","url":null,"abstract":"<div><p>In this paper, we study the regularizing effects of a singular first-order term in some degenerate elliptic equations with zero-order term involving Hardy potential. The model problem is </p><div><div><span>$$begin{aligned}begin{aligned} left{ begin{array}{ll} -textrm{div}left( frac{vert nabla uvert ^{p-2}nabla u}{(1+|u|)^{gamma }}right) +frac{vert nabla uvert ^{p}}{u^{theta }}=frac{u^{r}}{vert xvert ^{p}}+f &amp;{}text{ in } Omega , u&gt;0&amp;{} text{ in } Omega , u=0&amp;{} text{ on } partial Omega , end{array}right. end{aligned}end{aligned}$$</span></div></div><p>where <span>(Omega )</span> is a bounded open subset in <span>({mathbb {R}}^{N})</span> with <span>(0in Omega )</span>, <span>(gamma ge 0)</span>, <span>(1&lt;p&lt;N)</span>, <span>(0&lt;theta &lt;1)</span>, and <span>(0&lt;r&lt;p-theta )</span>. We prove existence and regularity results for solutions under various hypotheses on the datum <i>f</i>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140242743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Best approximations in metric spaces with property strongly UC 具有强 UC 属性的度量空间中的最佳近似值
IF 0.8
Advances in Operator Theory Pub Date : 2024-03-12 DOI: 10.1007/s43036-024-00323-y
Abhik Digar
{"title":"Best approximations in metric spaces with property strongly UC","authors":"Abhik Digar","doi":"10.1007/s43036-024-00323-y","DOIUrl":"10.1007/s43036-024-00323-y","url":null,"abstract":"<div><p>In this article, we introduce a geometrical notion, called property strongly UC which is stronger than property UC and prove the existence of best approximations for a new class of almost cyclic <span>(psi)</span>-contraction maps defined on a pair of subsets of a metric space. As a particular case of this existence theorem, we obtain the main results of [Sadiq Basha, S., Best approximation theorems for almost cyclic contractions. J. Fixed Point Theory Appl. 23 (2021)] and [Eldred, A. Anthony; Veeramani, P., Existence and convergence of best proximity points. J. Math. Anal. Appl. 323 (2006)]. Moreover, we study the existence of a best approximation and continuity properties of almost cyclic contractions in the context of a reflexive Banach space and a metric space.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411502","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Interpolating numerical radius inequalities for matrices 矩阵数值半径不等式的内插法
IF 0.8
Advances in Operator Theory Pub Date : 2024-03-12 DOI: 10.1007/s43036-024-00325-w
Ahmad Al-Natoor, Omar Hirzallah, Fuad Kittaneh
{"title":"Interpolating numerical radius inequalities for matrices","authors":"Ahmad Al-Natoor,&nbsp;Omar Hirzallah,&nbsp;Fuad Kittaneh","doi":"10.1007/s43036-024-00325-w","DOIUrl":"10.1007/s43036-024-00325-w","url":null,"abstract":"<div><p>In this paper, we prove interpolating numerical radius inequalities involving the generalized numerical radii induced by unitarily invariant norms. These inequalities refine well-known interpolating norm inequalities. Several related numerical radius inequalities are also established.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140251171","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
KMS Dirichlet forms, coercivity and superbounded Markovian semigroups on von Neumann algebras KMS Dirichlet 形式、矫顽力和 von Neumann 对象上的超边界马尔可夫半群
IF 0.8
Advances in Operator Theory Pub Date : 2024-02-29 DOI: 10.1007/s43036-024-00315-y
Fabio E. G. Cipriani, Boguslaw Zegarlinski
{"title":"KMS Dirichlet forms, coercivity and superbounded Markovian semigroups on von Neumann algebras","authors":"Fabio E. G. Cipriani,&nbsp;Boguslaw Zegarlinski","doi":"10.1007/s43036-024-00315-y","DOIUrl":"10.1007/s43036-024-00315-y","url":null,"abstract":"<div><p>We introduce a construction of Dirichlet forms on von Neumann algebras <i>M</i> associated to any eigenvalue of the Araki modular Hamiltonian of a faithful normal non-tracial state, providing also conditions by which the associated Markovian semigroups are GNS symmetric. The structure of these Dirichlet forms is described in terms of spatial derivations. Coercivity bounds are proved and the spectral growth is derived. We introduce a regularizing property of positivity preserving semigroups (superboundedness) stronger than hypercontractivity, in terms of the symmetric embedding of <i>M</i> into its standard space <span>(L^2(M))</span> and the associated noncommutative <span>(L^p(M))</span> spaces. We prove superboundedness for a special class of positivity preserving semigroups and that some of them are dominated by the Markovian semigroups associated to the Dirichlet forms introduced above, for type I factors <i>M</i>. These tools are applied to a general construction of the quantum Ornstein–Uhlembeck semigroups of the Canonical Commutation Relations CCR and some of their non-perturbative deformations.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00315-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Singular value and unitarily invariant norm inequalities for matrices 矩阵的奇异值和单位不变规范不等式
IF 0.8
Advances in Operator Theory Pub Date : 2024-02-29 DOI: 10.1007/s43036-024-00319-8
Ahmad Al-Natoor, Omar Hirzallah, Fuad Kittaneh
{"title":"Singular value and unitarily invariant norm inequalities for matrices","authors":"Ahmad Al-Natoor,&nbsp;Omar Hirzallah,&nbsp;Fuad Kittaneh","doi":"10.1007/s43036-024-00319-8","DOIUrl":"10.1007/s43036-024-00319-8","url":null,"abstract":"<div><p>In this paper, we prove some new singular value and unitarily invariant norm inequalities for matrices. Among other results, it is shown that if <i>X</i>, <i>Y</i>, <i>Z</i>, <i>W</i> are <i>n</i> <span>(times )</span> <i>n</i> matrices, then </p><div><div><span>$$begin{aligned} s_{j}left( XY+ZWright) le textrm{max}left( left| Yright| ,left| Zright| right) s_{j}left( Xoplus Wright) +frac{1}{2} left| XY+ZWright| end{aligned}$$</span></div></div><p>and </p><div><div><span>$$begin{aligned} Vert XYpm YXVert le Vert XVert Vert YVert +w(XY) end{aligned}$$</span></div></div><p>for <span>(j=1,2,ldots ,n)</span>, where <span>(left| cdot right| ,w(cdot ),)</span> and <span>( s_{j}(cdot ))</span> denote the spectral norm, the numerical radius, and the <i>j</i>th singular value of matrices.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140408681","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Linearity of (generalized) (*)-Lie derivations and their structures on (*)-algebras $$*$$-Lie（广义）派生的线性及其在 $$*$$-gebras 上的结构
IF 0.8
Advances in Operator Theory Pub Date : 2024-02-27 DOI: 10.1007/s43036-024-00320-1
Behrooz Fadaee, Hoger Ghahramani, Wu Jing
{"title":"Linearity of (generalized) (*)-Lie derivations and their structures on (*)-algebras","authors":"Behrooz Fadaee,&nbsp;Hoger Ghahramani,&nbsp;Wu Jing","doi":"10.1007/s43036-024-00320-1","DOIUrl":"10.1007/s43036-024-00320-1","url":null,"abstract":"<div><p>Let <span>( {mathcal {A}} )</span> be a unital <span>(*)</span>-algebra with characteristic not 2 and containing a nontrivial projection. We show that each nonlinear <span>(*)</span>-Lie derivation on <span>({mathcal {A}})</span> is a linear <span>(*)</span>-derivation. Moreover, we characterize nonlinear left <span>(*)</span>-Lie centralizers and nonlinear generalized <span>(*)</span>-Lie derivations. These results are applied to standard operator algebras and von Neumann algebras in complex Hilbert spaces, which generalize some known results.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140427023","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Convex decompositions of Q-stochastic tensors and Bell locality in a multipartite system Q-随机张量的凸分解和多方系统中的贝尔位置性
IF 0.8
Advances in Operator Theory Pub Date : 2024-02-27 DOI: 10.1007/s43036-024-00316-x
Huai-Xin Cao, Hong-Yi Chen, Zhi-Hua Guo, Tsung-Lin Lee, Ngai-Ching Wong
{"title":"Convex decompositions of Q-stochastic tensors and Bell locality in a multipartite system","authors":"Huai-Xin Cao,&nbsp;Hong-Yi Chen,&nbsp;Zhi-Hua Guo,&nbsp;Tsung-Lin Lee,&nbsp;Ngai-Ching Wong","doi":"10.1007/s43036-024-00316-x","DOIUrl":"10.1007/s43036-024-00316-x","url":null,"abstract":"<div><p>Generalizing the notions of the row and the column stochastic matrices, we introduce the multidimensional <i>Q</i>-stochastic tensors. We prove that every <i>Q</i>-stochastic tensor can be decomposed as a convex combination of finitely many binary <i>Q</i>-stochastic tensors and that the binary <i>Q</i>-stochastic tensors are exactly the extreme points of the compact convex set of all <i>Q</i>-stochastic tensors with the same size. Applications to characterizing the Bell locality of a quantum state in a multipartite system are demonstrated. Algorithms for computing the convex decompositions of <i>Q</i>-stochastic tensors are provided.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140425840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some relationships between an operator and its transform (S_{r}(T)) 算子与其变换 $$S_{r}(T)$$ 之间的一些关系
IF 0.8
Advances in Operator Theory Pub Date : 2024-02-22 DOI: 10.1007/s43036-024-00317-w
Safa Menkad, Sohir Zid
{"title":"Some relationships between an operator and its transform (S_{r}(T))","authors":"Safa Menkad,&nbsp;Sohir Zid","doi":"10.1007/s43036-024-00317-w","DOIUrl":"10.1007/s43036-024-00317-w","url":null,"abstract":"<div><p>Let <span>( T in mathcal {B}(mathcal {H}))</span> be a bounded linear operator on a Hilbert space <span>( mathcal {H})</span>, and let <span>( T = U vert T vert )</span> be the polar decomposition of <i>T</i>. For any <span>(r &gt; 0)</span>, the transform <span>(S_{r}(T))</span> is defined by <span>(S_{r}(T) = U vert T vert ^{r} U)</span>. In this paper, we discuss the transform <span>(S_{r}(T))</span> of some classes of operators such as p-hyponormal and rank one operators. We provide a new characterization of invertible normal operators via this transform. Afterwards, we investigate when an operator <i>T</i> and its transform <span>( S_{r}(T) )</span> both have closed ranges, and show that this transform preserves the class of EP operators. Finally, we present some relationships between an EP operator <i>T</i>, its transform <span>( S_{r}(T))</span> and the Moore–Penrose inverse <span>( T^{+} )</span>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140439291","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","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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