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On the geometry of the Birkhoff polytope I: the operator (ell ^p_n)-norms 关于伯克霍夫多胞形的几何 I：算子 $$ell ^p_n$ 元矩阵
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-07-20 DOI: 10.1007/s44146-024-00152-8
Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin
{"title":"On the geometry of the Birkhoff polytope I: the operator (ell ^p_n)-norms","authors":"Ludovick Bouthat,&nbsp;Javad Mashreghi,&nbsp;Frédéric Morneau-Guérin","doi":"10.1007/s44146-024-00152-8","DOIUrl":"10.1007/s44146-024-00152-8","url":null,"abstract":"<div><p>The geometry of the Birkhoff polytope, i.e., the compact convex set of all <span>(n times n)</span> doubly stochastic matrices, has been an active subject of research. While its faces, edges and facets as well as its volume have been intensely studied, other geometric characteristics such as the center and radius were left off, despite their natural uses in some areas of mathematics. In this paper, we completely characterize the Chebyshev center and the Chebyshev radius of the Birkhoff polytope associated with the metrics induced by the operator <span>(ell ^p_n)</span>-norms for the range <span>(1 le p le infty )</span>.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"91 1-2","pages":"227 - 245"},"PeriodicalIF":0.5,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141819366","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 the Birkhoff polytope II: the Schatten p-norms 关于伯克霍夫多胞几何 II：沙腾 p 准则
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-07-18 DOI: 10.1007/s44146-024-00153-7
Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin
{"title":"On the geometry of the Birkhoff polytope II: the Schatten p-norms","authors":"Ludovick Bouthat, Javad Mashreghi, Frédéric Morneau-Guérin","doi":"10.1007/s44146-024-00153-7","DOIUrl":"https://doi.org/10.1007/s44146-024-00153-7","url":null,"abstract":"","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":" 9","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141827571","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
Operator means and the reduced relative quantum entropy 运算符手段和缩小的相对量子熵
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-07-18 DOI: 10.1007/s44146-024-00149-3
Frank Hansen
{"title":"Operator means and the reduced relative quantum entropy","authors":"Frank Hansen","doi":"10.1007/s44146-024-00149-3","DOIUrl":"10.1007/s44146-024-00149-3","url":null,"abstract":"<div><p>We study operator means more general than the Kubo-Ando means. They are given as minima of geodesically convex functions and allow uniquely defined extensions to any number of variables. Multivariate hyper-means is a class of means of this type bounded from below by the arithmetic mean. We extend the definition of a hyper-man in the bivariate case and discover bivariate means that are not restrictions of the multivariate means studied earlier. We introduce the notion of reduced relative quantum entropy and prove that it is convex. The result is used to give a simplified proof of a theorem of Lieb and Seiringer.\u0000</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 3-4","pages":"565 - 574"},"PeriodicalIF":0.5,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s44146-024-00149-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141827384","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
(Delta _{{{varvec{i}}}_{g}})-invertible operators I $$Delta _{{{varvec{i}}}_{g}}$$ 不可逆算子 I
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-07-16 DOI: 10.1007/s44146-024-00151-9
Asma Lahmar, Haïkel Skhiri
{"title":"(Delta _{{{varvec{i}}}_{g}})-invertible operators I","authors":"Asma Lahmar,&nbsp;Haïkel Skhiri","doi":"10.1007/s44146-024-00151-9","DOIUrl":"10.1007/s44146-024-00151-9","url":null,"abstract":"<div><p>Inspired by generalized invertibility, Drazin invertibility and some recent works (Lahmar and Skhiri in Pseudo-generalized inverse I, 2022; Pseudo-generalized inverse II, 2022; Results Math 78:24, 2023; Acta Sci. Math. (Szeged) 89:389–411, 2023), this paper explores a novel class of operators called <span>(Delta _{{{varvec{i}}}_{g}})</span>-invertible operators including all the mentioned concepts. Due to this extension, we successfully introduce a new concept of inverse that extends various inverse concepts, such as Drazin inverse, group inverse, Moore-Penrose inverse and DPG inverses, establishing a unified framework for all these concepts. We discuss several properties of this new inverse such as its uniqueness and outer inverse nature. In the context of Hilbert space, we present a specific case in which several properties of the Moore-Penrose inverse remain valid. As an application of our new concept, we prove various properties and perturbation results related to the pseudo-generalized invertibility introduced in (Lahmar and Skhiri in Pseudo-generalized inverse I, 2022).</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"91 1-2","pages":"267 - 293"},"PeriodicalIF":0.5,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141643746","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
Operator means, barycenters, and fixed point equations 运算符手段、原点和定点方程
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-07-15 DOI: 10.1007/s44146-024-00148-4
Dániel Virosztek
{"title":"Operator means, barycenters, and fixed point equations","authors":"Dániel Virosztek","doi":"10.1007/s44146-024-00148-4","DOIUrl":"10.1007/s44146-024-00148-4","url":null,"abstract":"<div><p>The seminal work of Kubo and Ando (Math Ann 246:205–224, 1979/80) provided us with an axiomatic approach to means of positive operators. As most of their axioms are algebraic in nature, this approach has a clear algebraic flavour. On the other hand, it is highly natural to take the geomeric viewpoint and consider a distance (understood in a broad sense) on the cone of positive operators, and define the mean of positive operators by an appropriate notion of the center of mass. This strategy often leads to a fixed point equation that characterizes the mean. The aim of this survey is to highlight those cases where the algebraic and the geometric approaches meet each other.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 3-4","pages":"391 - 408"},"PeriodicalIF":0.5,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s44146-024-00148-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141645452","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
Some numerical radius bounds 一些数值半径界限
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-07-14 DOI: 10.1007/s44146-024-00150-w
Satyajit Sahoo, H. Moradi, M. Sababheh
{"title":"Some numerical radius bounds","authors":"Satyajit Sahoo, H. Moradi, M. Sababheh","doi":"10.1007/s44146-024-00150-w","DOIUrl":"https://doi.org/10.1007/s44146-024-00150-w","url":null,"abstract":"","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"52 6","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141650536","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
Lattice properties of strength functions 强度函数的晶格特性
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-07-14 DOI: 10.1007/s44146-024-00146-6
Andriamanankasina Ramanantoanina, Tamás Titkos
{"title":"Lattice properties of strength functions","authors":"Andriamanankasina Ramanantoanina,&nbsp;Tamás Titkos","doi":"10.1007/s44146-024-00146-6","DOIUrl":"10.1007/s44146-024-00146-6","url":null,"abstract":"<div><p>This paper investigates an important functional representation of the cone of bounded positive semidefinite operators. It is known that the representation by strength functions turns the Löwner order into the pointwise order. However, very little is known about the structure of strength functions. Our main result says that the representation behaves naturally with the infimum and supremum operations. More precisely, we show that the pointwise minimum of two strength functions <span>(f_A)</span> and <span>(f_B)</span> is a strength function if and only if the infimum of <i>A</i> and <i>B</i> exists. This complements a recent result of L. Molnár stating that the pointwise maximum of <span>(f_A)</span> and <span>(f_B)</span> exists if and only if <i>A</i> and <i>B</i> are comparable, as this latter statement is equivalent to the existence of the supremum. The cornerstone of each argument in this paper is a fact that was discovered recently, namely that the strength function of the parallel sum <i>A</i> : <i>B</i> (which is half of the harmonic mean) equals the parallel sum of the strength functions <span>(f_A)</span> and <span>(f_B)</span>. We provide a new proof for this statement, and as a byproduct, in some special cases, we describe the strength function of the so-called (generalized) short.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 3-4","pages":"679 - 689"},"PeriodicalIF":0.5,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s44146-024-00146-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141650340","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
On S-Weyl’s theorem and property (t) for some classes of operators 关于某些类算子的 S-韦尔定理和性质 (t)
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-07-10 DOI: 10.1007/s44146-024-00147-5
Pietro Aiena, Fabio Burderi, Salvatore Triolo
{"title":"On S-Weyl’s theorem and property (t) for some classes of operators","authors":"Pietro Aiena,&nbsp;Fabio Burderi,&nbsp;Salvatore Triolo","doi":"10.1007/s44146-024-00147-5","DOIUrl":"10.1007/s44146-024-00147-5","url":null,"abstract":"<div><p>In this paper we consider two new variants of the classical Weyl ’s theorem for operators defined on Banach spaces. These variants called <i>S</i>-Weyl’s theorem and property (<i>t</i>) are stronger than the more classical variants of Weyl’s theorem, as <i>a</i>-Weyl’s theorem and property <span>((omega ))</span> studied by several authors. In particular, we explore these two new variants for operators that commute with an injective quasi-nilpotent operators.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"91 1-2","pages":"295 - 312"},"PeriodicalIF":0.5,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141662678","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
Generating subspace lattices, their direct products, and their direct powers 生成子空间格，它们的直积，和它们的直幂
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-06-26 DOI: 10.1007/s44146-024-00145-7
Gábor Czédli
{"title":"Generating subspace lattices, their direct products, and their direct powers","authors":"Gábor Czédli","doi":"10.1007/s44146-024-00145-7","DOIUrl":"10.1007/s44146-024-00145-7","url":null,"abstract":"<div><p>In 2008, László Zádori proved that the lattice <span>(Sub (V) )</span> of all subspaces of a vector space <i>V</i> of finite dimension at least 3 over a finite field <i>F</i> has a 5-element generating set; in other words, <span>(Sub (V) )</span> is 5-generated. We prove that the same holds over every 1- or 2-generated field; in particular, over every field that is a finite degree extension of its prime field. Furthermore, let <i>F</i>, <i>t</i>, <i>V</i>, <span>(dge 3)</span>, <span>(lfloor d/2rfloor )</span>, and <i>m</i> denote an arbitrary field, the minimum cardinality of a generating set of <i>F</i>, a finite dimensional vector space over <i>F</i>, the dimension (assumed to be at least 3) of <i>V</i>, the integer part of <i>d</i>/2, and the least cardinal such that <span>(mlfloor d^2/4rfloor )</span> is at least <i>t</i>, respectively. We prove that <span>(Sub (V) )</span> is <span>((4+m))</span>-generated but none of its generating sets is of size less than <i>m</i>. Moreover, the <i>k</i>th direct power of <span>(Sub (V) )</span> is <span>((5+m))</span>-generated for many positive integers <i>k</i>; for all positive integers <i>k</i> if <i>F</i> is infinite. Finally, let <i>n</i> be a positive integer. For <span>(i=1,dots , n)</span>, let <span>(p_i)</span> be a prime number or 0, and let <span>(V_i)</span> be the 3-dimensional vector space over the prime field of characteristic <span>(p_i)</span>. We prove that the direct product of the lattices <span>(Sub (V_1) )</span>, ..., <span>(Sub (V_n) )</span> is 4-generated if and only if each of the numbers <span>(p_1)</span>, ..., <span>(p_n)</span> occurs at most four times in the sequence <span>(p_1)</span>, ..., <span>(p_n)</span>. Neither this direct product nor any of the subspace lattices <span>(Sub (V) )</span> above is 3-generated.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"91 1-2","pages":"23 - 55"},"PeriodicalIF":0.5,"publicationDate":"2024-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143938724","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
Symmetric operator means 对称算子均值
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-06-24 DOI: 10.1007/s44146-024-00141-x
Mitsuru Uchiyama
{"title":"Symmetric operator means","authors":"Mitsuru Uchiyama","doi":"10.1007/s44146-024-00141-x","DOIUrl":"10.1007/s44146-024-00141-x","url":null,"abstract":"<div><p>The purpose of this paper is to extend symmetric means of multi-variable positive matrices to those of multi-variable positive operators on an infinite dimensional Hilbert space. We also consider the situations where symmetric means of operators <i>A</i>, <i>B</i>, <i>C</i> become linear combinations of them.\u0000</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 3-4","pages":"593 - 604"},"PeriodicalIF":0.5,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s44146-024-00141-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826203","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
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