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Advances in Operator Theory最新文献

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Truncations of operators in ({mathcal {B}}({mathcal {H}})) and their preservers $${mathcal {B}}({mathcal {H}})$$中算子的截断及其保值器
IF 0.8
Advances in Operator Theory Pub Date : 2024-04-03 DOI: 10.1007/s43036-024-00332-x
Yanling Mao, Guoxing Ji
{"title":"Truncations of operators in ({mathcal {B}}({mathcal {H}})) and their preservers","authors":"Yanling Mao,&nbsp;Guoxing Ji","doi":"10.1007/s43036-024-00332-x","DOIUrl":"10.1007/s43036-024-00332-x","url":null,"abstract":"<div><p>Let <span>(mathcal {H})</span> be a complex Hilbert space with <span>(dim {mathcal {H}}ge 2)</span> and <span>(mathcal {B}(mathcal {H}))</span> be the algebra of all bounded linear operators on <span>(mathcal {H})</span>. For <span>(A, B in mathcal {B}(mathcal {H}))</span>, <i>B</i> is called a truncation of <i>A</i>, denoted by <span>(Bprec A)</span>, if <span>(B=PAQ)</span> for some projections <span>(P,Qin {mathcal {B}}({mathcal {H}}))</span>. And <i>B</i> is called a maximal truncation of <i>A</i> if <span>(Bnot =A)</span> and there is no other truncation <i>C</i> of <i>A</i> such that <span>(Bprec C)</span>. We give necessary and sufficient conditions for <i>B</i> to be a maximal truncation of <i>A</i>. Using these characterizations, we determine structures of all bijections preserving truncations of operators in both directions on <span>(mathcal {B}(mathcal {H}))</span>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140760160","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
Fejér–Riesz factorization in the QRC-subalgebra and circularity of the quaternionic numerical range QRC 子代数中的 Fejér-Riesz 因式分解和四元数程的圆周性
IF 0.8
Advances in Operator Theory Pub Date : 2024-04-03 DOI: 10.1007/s43036-024-00330-z
Alma van der Merwe, Madelein van Straaten, Hugo J. Woerdeman
{"title":"Fejér–Riesz factorization in the QRC-subalgebra and circularity of the quaternionic numerical range","authors":"Alma van der Merwe,&nbsp;Madelein van Straaten,&nbsp;Hugo J. Woerdeman","doi":"10.1007/s43036-024-00330-z","DOIUrl":"10.1007/s43036-024-00330-z","url":null,"abstract":"<div><p>We provide a characterization when the quaternionic numerical range of a matrix is a closed ball with center 0. The proof makes use of Fejér–Riesz factorization of matrix-valued trigonometric polynomials within the algebra of complex matrices associated with quaternion matrices.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-024-00330-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140783695","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
Frame dimension functions and phase retrievability 帧维函数和相位检索
IF 0.8
Advances in Operator Theory Pub Date : 2024-04-03 DOI: 10.1007/s43036-024-00331-y
Deguang Han, Kai Liu
{"title":"Frame dimension functions and phase retrievability","authors":"Deguang Han,&nbsp;Kai Liu","doi":"10.1007/s43036-024-00331-y","DOIUrl":"10.1007/s43036-024-00331-y","url":null,"abstract":"<div><p>The frame dimension function of a frame <span>({{mathcal {F}}}= {f_j}_{j=1}^{n})</span> for an <i>n</i>-dimensional Hilbert space <i>H</i> is the function <span>(d_{{{mathcal {F}}}}(x) = dim {textrm{span}}{ langle x, f_{j}rangle f_{j}: j=1,ldots , N}, 0ne xin H.)</span> It is known that <span>({{mathcal {F}}})</span> does phase retrieval for an <i>n</i>-dimensional real Hilbert space <i>H</i> if and only if <span>({textrm{range}} (d_{{{mathcal {F}}}}) = { n}.)</span> This indicates that the range of the dimension function is one of the good candidates to measure the phase retrievability for an arbitrary frame. In this paper we investigate some structural properties for the range of the dimension function, and examine the connections among different exactness of a frame with respect to its PR-redundance, dimension function and range of the dimension function. A subset <span>(Omega )</span> of <span>({1,ldots , n})</span> containing <i>n</i> is attainable if <span>({textrm{range}} (d_{{{mathcal {F}}}}) = Omega )</span> for some frame <span>({{mathcal {F}}}.)</span> With the help of linearly connected frames, we show that, while not every <span>(Omega )</span> is attainable, every (integer) interval containing <i>n</i> is always attainable by an <i>n</i>-linearly independent frame. Consequently, <span>({textrm{range}}(d_{{{mathcal {F}}}}))</span> is an interval for every generic frame for <span>({mathbb {R}},^n.)</span> Additionally, we also discuss and post some questions related to the connections among ranges of the dimension functions, linearly connected frames and maximal phase retrievable subspaces.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140771161","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
Numerical radius and geometric means of real power 实际功率的数值半径和几何平均数
IF 0.8
Advances in Operator Theory Pub Date : 2024-03-25 DOI: 10.1007/s43036-024-00328-7
Yuki Seo
{"title":"Numerical radius and geometric means of real power","authors":"Yuki Seo","doi":"10.1007/s43036-024-00328-7","DOIUrl":"10.1007/s43036-024-00328-7","url":null,"abstract":"<div><p>Norm inequalities related to geometric means are discussed by many researchers. Though the operator norm is unitarily invariant one, the numerical radius is not so and unitarily similar. In this paper, we prove some numerical radius inequalities that are related to operator geometric means and spectral geometric ones of real power for positive invertible operators.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140384228","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
On the geometry of an order unit space 关于阶单元空间的几何
IF 0.8
Advances in Operator Theory Pub Date : 2024-03-24 DOI: 10.1007/s43036-024-00327-8
Anil Kumar Karn
{"title":"On the geometry of an order unit space","authors":"Anil Kumar Karn","doi":"10.1007/s43036-024-00327-8","DOIUrl":"10.1007/s43036-024-00327-8","url":null,"abstract":"<div><p>We introduce the notion of <i>skeleton</i> with a head in a non-zero real vector space. We prove that skeletons with a head describe order unit spaces geometrically. Next, we prove that the skeleton consists of boundary elements of the positive cone of norm one. We discuss some elementary properties of the skeleton. We also find a condition under which <i>V</i> contains a copy of <span>(ell _{infty }^n)</span> for some <span>(n in {mathbb {N}})</span> as an order unit subspace.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"9 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413544","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
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
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