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Positivity最新文献

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Short note on some geometric inequalities derived from matrix inequalities 关于从矩阵不等式推导出的一些几何不等式的简短说明
IF 1 3区 数学
Positivity Pub Date : 2024-03-20 DOI: 10.1007/s11117-024-01042-7
{"title":"Short note on some geometric inequalities derived from matrix inequalities","authors":"","doi":"10.1007/s11117-024-01042-7","DOIUrl":"https://doi.org/10.1007/s11117-024-01042-7","url":null,"abstract":"<h3>Abstract</h3> <p>Using the connection between ellipsoids and positive semidefinite matrices we provide alternative proofs to some recently proven inequalities concerning the volume of <span> <span>(L_2)</span> </span> zonoids as consequences of classical inequalities for matrices.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168675","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
Discrete stopping times in the lattice of continuous functions 连续函数网格中的离散停止时间
IF 1 3区 数学
Positivity Pub Date : 2024-03-19 DOI: 10.1007/s11117-024-01044-5
Achintya Raya Polavarapu
{"title":"Discrete stopping times in the lattice of continuous functions","authors":"Achintya Raya Polavarapu","doi":"10.1007/s11117-024-01044-5","DOIUrl":"https://doi.org/10.1007/s11117-024-01044-5","url":null,"abstract":"<p>A functional calculus for an order complete vector lattice <span>({mathcal {E}})</span> was developed by Grobler (Indag Math (NS) 25(2):275–295, 2014) using the Daniell integral. We show that if one represents the universal completion of <span>({mathcal {E}})</span> as <span>(C^infty (K))</span>, where <i>K</i> is an extremally disconnected compact Hausdorff topological space, then the Daniell functional calculus for continuous functions is exactly the pointwise composition of functions in <span>(C^infty (K))</span>. This representation allows an easy deduction of the various properties of the functional calculus. Afterwards, we study discrete stopping times and stopped processes in <span>(C^infty (K))</span>. We obtain a representation that is analogous to what is expected in probability theory.\u0000</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140168487","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
Lebesgue spaces with variable exponent: some applications to the Navier–Stokes equations 具有可变指数的勒贝格空间：纳维耶-斯托克斯方程的一些应用
IF 1 3区 数学
Positivity Pub Date : 2024-03-18 DOI: 10.1007/s11117-024-01043-6
Diego Chamorro, Gastón Vergara-Hermosilla
{"title":"Lebesgue spaces with variable exponent: some applications to the Navier–Stokes equations","authors":"Diego Chamorro, Gastón Vergara-Hermosilla","doi":"10.1007/s11117-024-01043-6","DOIUrl":"https://doi.org/10.1007/s11117-024-01043-6","url":null,"abstract":"<p>In this article we study some problems related to the incompressible 3D Navier–Stokes equations from the point of view of Lebesgue spaces of variable exponent. These functional spaces present some particularities that make them quite different from the usual Lebesgue spaces: indeed, some of the most classical tools in analysis are not available in this framework. We will give here some ideas to overcome some of the difficulties that arise in this context in order to obtain different results related to the existence of mild solutions for this evolution problem.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152155","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 results about order Fredholm theory in Banach lattices 关于巴拿赫网格中阶弗雷德霍姆理论的一些新结果
IF 1 3区 数学
Positivity Pub Date : 2024-03-16 DOI: 10.1007/s11117-024-01038-3
Youssef Ezzaki, Othman Aboutafail, Jawad H’michane
{"title":"Some new results about order Fredholm theory in Banach lattices","authors":"Youssef Ezzaki, Othman Aboutafail, Jawad H’michane","doi":"10.1007/s11117-024-01038-3","DOIUrl":"https://doi.org/10.1007/s11117-024-01038-3","url":null,"abstract":"<p>This paper aims to introduce and study a new generalized class of semi-Fredholm operators acting between Banach lattices called order semi-Fredholm operators. It highlights some interesting properties of this class. Also, a perturbation properties are obtained. Finally, we discuss the conditions that make the adjoint of an order semi-Fredholm operator be a semi-Fredholm operator.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152151","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 spectra of some completely positive maps 关于一些完全正映射的光谱
IF 1 3区 数学
Positivity Pub Date : 2024-03-15 DOI: 10.1007/s11117-024-01037-4
Yuan Li, Shuhui Gao, Cong Zhao, Nan Ma
{"title":"On spectra of some completely positive maps","authors":"Yuan Li, Shuhui Gao, Cong Zhao, Nan Ma","doi":"10.1007/s11117-024-01037-4","DOIUrl":"https://doi.org/10.1007/s11117-024-01037-4","url":null,"abstract":"<p>Let <span>(sum _{i=1}^{infty }A_iA_i^*)</span> and <span>(sum _{i=1}^{infty }A_i^*A_i)</span> converge in the strong operator topology. We study the map <span>(Phi _{{mathcal {A}}})</span> defined on the Banach space of all bounded linear operators <span>({mathcal {B(H)}})</span> by <span>(Phi _{{mathcal {A}}}(X)=sum _{i=1}^{infty }A_iXA_i^*)</span> and its restriction <span>(Phi _{{mathcal {A}}}|_{mathcal {K(H})})</span> to the Banach space of all compact operators <span>(mathcal {K(H)}.)</span> We first consider the relationship between the boundary eigenvalues of <span>(Phi _{{mathcal {A}}}|_{mathcal {K(H})})</span> and its fixed points. Also, we show that the spectra of <span>(Phi _{{mathcal {A}}})</span> and <span>(Phi _{{mathcal {A}}}|_{mathcal {K(H})})</span> are the same sets. In particular, the spectra of two completely positive maps involving the unilateral shift are described.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152157","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
Partial trace inequalities for partial transpose of positive semidefinite block matrices 正半有限块矩阵部分转置的部分迹不等式
IF 1 3区 数学
Positivity Pub Date : 2024-03-14 DOI: 10.1007/s11117-024-01039-2
Junjian Yang, Huan Xu
{"title":"Partial trace inequalities for partial transpose of positive semidefinite block matrices","authors":"Junjian Yang, Huan Xu","doi":"10.1007/s11117-024-01039-2","DOIUrl":"https://doi.org/10.1007/s11117-024-01039-2","url":null,"abstract":"<p>Li (Algebra 71:2823–2838, 2023) recently obtained several improvements on some partial trace inequalities for positive semidefinite block matrices. In this note, we present analogous partial trace inequalities involving partial transpose of positive semidefinite block matrix. The inequalities we show could be regarded as complements of Li’s results. In addition, some new partial trace inequalities for partial transpose of positive semidefinite block matrix are included.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125806","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 almost limited p-convergent operators on Banach lattices 论巴拿赫网格上几乎有限的 p-convergent 算子
IF 1 3区 数学
Positivity Pub Date : 2024-03-14 DOI: 10.1007/s11117-024-01040-9
H. Ardakani, F. Vali
{"title":"On almost limited p-convergent operators on Banach lattices","authors":"H. Ardakani, F. Vali","doi":"10.1007/s11117-024-01040-9","DOIUrl":"https://doi.org/10.1007/s11117-024-01040-9","url":null,"abstract":"<p>The purpose of this article is to introduce and study the class of almost limited <i>p</i>-convergent and weak<span>(^*)</span> almost <i>p</i>-convergent operators (<span>(1 le p &lt;infty )</span>). Some new characterizations of Banach lattices with the strong limited <i>p</i>-Schur property; that is, spaces on which every almost limited weakly <i>p</i>-compact set is relatively compact and the weak DP<span>(^*)</span> property of order <i>p</i> are obtained. The behavior of the class of these operators with the weak DP<span>(^*)</span> property of order <i>p</i> (with focus on Banach lattices with the strong limited <i>p</i>-Schur property) is investigated. Moreover, Banach lattices with the positive limited <i>p</i>-Schur property are introduced and Banach lattices in which this property is equivalent to some other known properties are discussed. In addition, the domination properties of almost limited <i>p</i>-convergent and weak<span>(^*)</span> almost <i>p</i>-convergent operators are considered. As an application, using almost limited <i>p</i>-convergent operators we establish some necessary and sufficient conditions under which some operator spaces have the strong limited <i>p</i>-Schur property.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125839","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
Robust optimality and duality for composite uncertain multiobjective optimization in Asplund spaces with its applications Asplund 空间中复合不确定多目标优化的稳健最优性和对偶性及其应用
IF 1 3区 数学
Positivity Pub Date : 2024-03-08 DOI: 10.1007/s11117-024-01032-9
Maryam Saadati, Morteza Oveisiha
{"title":"Robust optimality and duality for composite uncertain multiobjective optimization in Asplund spaces with its applications","authors":"Maryam Saadati, Morteza Oveisiha","doi":"10.1007/s11117-024-01032-9","DOIUrl":"https://doi.org/10.1007/s11117-024-01032-9","url":null,"abstract":"<p>This article is devoted to investigate a nonsmooth/nonconvex uncertain multiobjective optimization problem with composition fields (<span>((text {CUP}))</span> for brevity) over arbitrary Asplund spaces. Employing some advanced techniques of variational analysis and generalized differentiation, we establish necessary optimality conditions for weakly robust efficient solutions of <span>((text {CUP}))</span> in terms of the limiting subdifferential. Sufficient conditions for the existence of (weakly) robust efficient solutions to such a problem are also driven under the new concept of pseudo-quasi convexity for composite functions. We formulate a Mond–Weir-type robust dual problem to the primal problem <span>((text {CUP}))</span>, and explore weak, strong, and converse duality properties. In addition, the obtained results are applied to an approximate uncertain multiobjective problem and a composite uncertain multiobjective problem with linear operators.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140070215","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 the norm bounded sets of the ideal $$E^{a}$$ 关于理想$$E^{a}$$的规范有界集
IF 1 3区 数学
Positivity Pub Date : 2024-03-04 DOI: 10.1007/s11117-024-01036-5
{"title":"On the norm bounded sets of the ideal $$E^{a}$$","authors":"","doi":"10.1007/s11117-024-01036-5","DOIUrl":"https://doi.org/10.1007/s11117-024-01036-5","url":null,"abstract":"<h3>Abstract</h3> <p>The paper is devoted to study the norm bounded subsets which are contained in <span> <span>(E^{a})</span> </span>. Also, we introduce and study the class of the bounded-<span> <span>(E^a)</span> </span> operators, which maps the closed unit ball of a Banach space to a subset of <span> <span>(E^{a})</span> </span>. Some interesting results about this class of operators are presented.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140035645","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 results on upper semi-Fredholm operators on Banach lattices 关于巴拿赫网格上半弗雷德霍尔姆算子的一些结果
IF 1 3区 数学
Positivity Pub Date : 2024-02-29 DOI: 10.1007/s11117-024-01030-x
Youssef Ezzaki, Redouane Nouira, Othman Aboutafail
{"title":"Some results on upper semi-Fredholm operators on Banach lattices","authors":"Youssef Ezzaki, Redouane Nouira, Othman Aboutafail","doi":"10.1007/s11117-024-01030-x","DOIUrl":"https://doi.org/10.1007/s11117-024-01030-x","url":null,"abstract":"<p>We study the class of upper semi-Fredholm operators acting between Banach lattices. It focuses on the domination of such operators by compact, Dunford–Pettis and AM-compact operators.\u0000</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140009989","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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