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Spectrum of weighted composition operators part X: the spectrum and essential spectra of weighted automorphisms of the polydisc algebra 加权合成算子谱第 X 部分：多圆盘代数的加权自动形的谱和本质谱
IF 1 3区 数学
Positivity Pub Date : 2024-07-29 DOI: 10.1007/s11117-024-01069-w
Arkady Kitover, Mehmet Orhon
{"title":"Spectrum of weighted composition operators part X: the spectrum and essential spectra of weighted automorphisms of the polydisc algebra","authors":"Arkady Kitover, Mehmet Orhon","doi":"10.1007/s11117-024-01069-w","DOIUrl":"https://doi.org/10.1007/s11117-024-01069-w","url":null,"abstract":"<p>We investigate the spectrum and the essential spectra of weighted automorphisms of the polydisc algebra <span>(mathbb {A}^n)</span>. In the case <span>(n=2)</span> we provide a detailed and, in most cases, complete description of these spectra.\u0000</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141871478","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
Non-linear traces on semifinite factors and generalized singular values 半有限因子上的非线性迹线和广义奇异值
IF 1 3区 数学
Positivity Pub Date : 2024-07-24 DOI: 10.1007/s11117-024-01073-0
Masaru Nagisa, Yasuo Watatani
{"title":"Non-linear traces on semifinite factors and generalized singular values","authors":"Masaru Nagisa, Yasuo Watatani","doi":"10.1007/s11117-024-01073-0","DOIUrl":"https://doi.org/10.1007/s11117-024-01073-0","url":null,"abstract":"<p>We introduce non-linear traces of the Choquet type and Sugeno type on a semifinite factor <span>(mathcal {M})</span> as a non-commutative analog of the Choquet integral and Sugeno integral for non-additive measures. We need a weighted dimension function <span>(p mapsto alpha (tau (p)))</span> for projections <span>(p in mathcal {M})</span>, which is an analog of a monotone measure. They have certain partial additivities. We show that these partial additivities characterize non-linear traces of both the Choquet type and Sugeno type, respectively. Based on the notion of generalized eigenvalues and singular values, we show that non-linear traces of the Choquet type are closely related to the Lorentz function spaces and the Lorentz operator spaces if the weight functions <span>(alpha )</span> are concave. For the algebras of compact operators and factors of type <span>(textrm{II})</span>, we completely determine the condition that the associated weighted <span>(L^p)</span>-spaces for the non-linear traces become quasi-normed spaces in terms of the weight functions <span>(alpha )</span> for any <span>(0&lt; p &lt; infty )</span>. We also show that any non-linear trace of the Sugeno type yields a certain metric on the factor. This is an attempt at non-linear and non-commutative integration theory on semifinite factors.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141781620","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
Weak fixed point property of order p in Banach lattices 巴拿赫网格中 p 阶的弱定点性质
IF 1 3区 数学
Positivity Pub Date : 2024-07-23 DOI: 10.1007/s11117-024-01074-z
H. Ardakani, K. Fallahi, S. Rajavzade
{"title":"Weak fixed point property of order p in Banach lattices","authors":"H. Ardakani, K. Fallahi, S. Rajavzade","doi":"10.1007/s11117-024-01074-z","DOIUrl":"https://doi.org/10.1007/s11117-024-01074-z","url":null,"abstract":"<p>The concept of weak orthogonality of order <i>p</i> (<span>(1 le p le infty )</span>) in Banach lattices is introduced in order to obtain spaces with the weak fixed point property of order <i>p</i>. Moreover, various connections between a number of Banach space properties to imply the weak fixed point property, such as Opial condition, weak normal structure and property (M) are investigated. In particular, it is established that for each Banach space <i>X</i> and a suitable Banach lattice <i>F</i>, a Banach lattice <span>(mathcal {M}subset K(X,F))</span> has the weak fixed point property of order <i>p</i>, if each evaluation operator <span>(psi _{y^*})</span> on <span>(mathcal {M})</span> is a <i>p</i>-convergent operator for <span>(y^*in F^*)</span>.\u0000</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141781621","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
Polynomial-like iterative equation on Riesz spaces 里兹空间上的多项式迭代方程
IF 1 3区 数学
Positivity Pub Date : 2024-07-22 DOI: 10.1007/s11117-024-01072-1
Chaitanya Gopalakrishna, Weinian Zhang
{"title":"Polynomial-like iterative equation on Riesz spaces","authors":"Chaitanya Gopalakrishna, Weinian Zhang","doi":"10.1007/s11117-024-01072-1","DOIUrl":"https://doi.org/10.1007/s11117-024-01072-1","url":null,"abstract":"<p>In this paper we investigate the polynomial-like iterative equation on Riesz spaces. Since a Riesz space does not need to have a metric space structure, neither the Schauder fixed point theorem nor the Banach fixed point theorem is available. Using the Knaster–Tarski fixed point theorem, we first obtain the existence and uniqueness of order-preserving solutions on convex complete sublattices of Riesz spaces. Then, restricting to <span>(mathbb {R})</span> and <span>(mathbb {R}^n)</span>, special cases of Riesz space, we obtain semi-continuous solutions and integrable solutions, respectively. Finally, we present more special cases of Riesz space in which solutions to the iterative equation can be discussed.\u0000</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141737519","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
A bound on the joint spectral radius using the diagonals 利用对角线的联合频谱半径约束
IF 1 3区 数学
Positivity Pub Date : 2024-07-18 DOI: 10.1007/s11117-024-01071-2
Vuong Bui
{"title":"A bound on the joint spectral radius using the diagonals","authors":"Vuong Bui","doi":"10.1007/s11117-024-01071-2","DOIUrl":"https://doi.org/10.1007/s11117-024-01071-2","url":null,"abstract":"<p>The primary aim of this paper is to establish bounds on the joint spectral radius for a finite set of nonnegative matrices based on their diagonal elements. The efficacy of this approach is evaluated in comparison to existing and related results in the field. In particular, let <span>(Sigma )</span> be any finite set of <span>(Dtimes D)</span> nonnegative matrices with the largest value <i>U</i> and the smallest value <i>V</i> over all positive entries. For each <span>(i=1,ldots ,D)</span>, let <span>(m_i)</span> be any number so that there exist <span>(A_1,ldots ,A_{m_i}in Sigma )</span> satisfying <span>((A_1ldots A_{m_i})_{i,i} &gt; 0)</span>, or let <span>(m_i=1)</span> if there are no such matrices. We prove that the joint spectral radius <span>(rho (Sigma ))</span> is bounded by </p><span>$$begin{aligned} begin{aligned}&amp;max _i root m_i of {max _{A_1,ldots ,A_{m_i}in Sigma } (A_1ldots A_{m_i})_{i,i}} le rho (Sigma ) &amp;quad le max _i root m_i of {left( frac{UD}{V}right) ^{3D^2} max _{A_1,ldots ,A_{m_i}in Sigma } (A_1ldots A_{m_i})_{i,i}}. end{aligned} end{aligned}$$</span>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141737599","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 maximal solid subspaces of intermediate algebras in C(X) 论 C(X) 中中间代数的最大实体子空间
IF 1 3区 数学
Positivity Pub Date : 2024-07-14 DOI: 10.1007/s11117-024-01067-y
J. M. Domínguez
{"title":"On maximal solid subspaces of intermediate algebras in C(X)","authors":"J. M. Domínguez","doi":"10.1007/s11117-024-01067-y","DOIUrl":"https://doi.org/10.1007/s11117-024-01067-y","url":null,"abstract":"<p>Let <i>C</i>(<i>X</i>) be the algebra of all real-valued continuous functions on a Tychonoff space <i>X</i>, and <span>(C^*(X))</span> the subalgebra of bounded functions. We prove that if <i>B</i> is any subalgebra of <i>C</i>(<i>X</i>) containing <span>(C^*(X))</span>, then no maximal solid subspace of <i>B</i> contains <span>(C^*(X))</span>, and we derive from this that the maximal solid subspaces of <i>B</i> are exactly the real maximal ideals of <i>B</i>. Then we extend the above to the case of intermediate algebras in <i>A</i>, where <i>A</i> is a <span>(varPhi )</span>-algebra with bounded inversion.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141612470","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
Positive definiteness of Hadamard exponentials and Hadamard inverses 哈达玛指数和哈达玛倒数的正定性
IF 1 3区 数学
Positivity Pub Date : 2024-07-13 DOI: 10.1007/s11117-024-01070-3
Takashi Sano
{"title":"Positive definiteness of Hadamard exponentials and Hadamard inverses","authors":"Takashi Sano","doi":"10.1007/s11117-024-01070-3","DOIUrl":"https://doi.org/10.1007/s11117-024-01070-3","url":null,"abstract":"<p>Let <i>A</i> be a positive semidefinite matrix. It is known that the Hadamard exponential of <i>A</i> is positive semidefinite; it is positive definite if and only if no two columns of <i>A</i> are identical. We give an alternative proof of the latter part with an application to Hadamard inverses.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141612469","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
Characterizations for the fractional maximal operator and its commutators on total Morrey spaces 总莫里空间上分数最大算子及其换元子的特征
IF 1 3区 数学
Positivity Pub Date : 2024-07-11 DOI: 10.1007/s11117-024-01068-x
V. S. Guliyev
{"title":"Characterizations for the fractional maximal operator and its commutators on total Morrey spaces","authors":"V. S. Guliyev","doi":"10.1007/s11117-024-01068-x","DOIUrl":"https://doi.org/10.1007/s11117-024-01068-x","url":null,"abstract":"<p>We shall give a characterization for the strong and weak type Adams type boundedness of the fractional maximal operator <span>(M_{alpha })</span> on total Morrey spaces <span>(L^{p,lambda ,mu }(mathbb {R}^n))</span>, respectively. Also we give necessary and sufficient conditions for the boundedness of the fractional maximal commutator operator <span>(M_{b,alpha })</span> and commutator of fractional maximal operator <span>([b,M_{alpha }])</span> on <span>(L^{p,lambda ,mu }(mathbb {R}^n))</span> when <i>b</i> belongs to <span>(BMO(mathbb {R}^n))</span> spaces, whereby some new characterizations for certain subclasses of <span>(BMO(mathbb {R}^n))</span> spaces are obtained.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141587240","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
Free uniformly complete vector lattices 自由均匀完整向量网格
IF 1 3区 数学
Positivity Pub Date : 2024-07-05 DOI: 10.1007/s11117-024-01066-z
Eduard Emelyanov, Svetlana Gorokhova
{"title":"Free uniformly complete vector lattices","authors":"Eduard Emelyanov, Svetlana Gorokhova","doi":"10.1007/s11117-024-01066-z","DOIUrl":"https://doi.org/10.1007/s11117-024-01066-z","url":null,"abstract":"<p>We define a free uniformly complete vector lattice <span>(text {FUCVL}(A))</span> over a non-empty set <i>A</i> and give its representation as a sublattice of the space <span>(H(mathbb {R}^A))</span> of continuous in the product topology positively homogeneous functions on <span>(mathbb {R}^A)</span>.\u0000</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141547693","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
Optimality conditions and duality for multiobjective semi-infinite optimization problems with switching constraints on Hadamard manifolds 哈达玛流形上带有切换约束的多目标半无限优化问题的最优条件和对偶性
IF 1 3区 数学
Positivity Pub Date : 2024-07-05 DOI: 10.1007/s11117-024-01065-0
Balendu Bhooshan Upadhyay, Arnav Ghosh
{"title":"Optimality conditions and duality for multiobjective semi-infinite optimization problems with switching constraints on Hadamard manifolds","authors":"Balendu Bhooshan Upadhyay, Arnav Ghosh","doi":"10.1007/s11117-024-01065-0","DOIUrl":"https://doi.org/10.1007/s11117-024-01065-0","url":null,"abstract":"<p>This paper deals with a certain class of multiobjective semi-infinite programming problems with switching constraints (in short, MSIPSC) in the framework of Hadamard manifolds. We introduce Abadie constraint qualification (in short, ACQ) for MSIPSC in the Hadamard manifold setting. Necessary criteria of weak Pareto efficiency for MSIPSC are derived by employing ACQ. Further, sufficient criteria of weak Pareto efficiency for MSIPSC are deduced by using geodesic quasiconvexity and pseudoconvexity assumptions. Subsequently, Mond–Weir type and Wolfe type dual models are formulated related to the primal problem MSIPSC, and thereafter, several duality results are established that relate MSIPSC and the corresponding dual models. Several non-trivial examples are furnished in the framework of well-known Hadamard manifolds, such as the set consisting of all symmetric positive definite matrices and the Poincaré half plane, to illustrate the importance of the results derived in this article. To the best of our knowledge, this is the first time that optimality conditions and duality results for MSIPSC have been studied in the setting of Hadamard manifolds.</p>","PeriodicalId":54596,"journal":{"name":"Positivity","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141577721","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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