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New characterizations of operator monotone functions 算子单调函数的新特征
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-11-26 DOI: 10.1007/s44146-024-00167-1
Bich Khue Vo, Trung Hoa Dinh, Hiroyuki Osaka
{"title":"New characterizations of operator monotone functions","authors":"Bich Khue Vo,&nbsp;Trung Hoa Dinh,&nbsp;Hiroyuki Osaka","doi":"10.1007/s44146-024-00167-1","DOIUrl":"10.1007/s44146-024-00167-1","url":null,"abstract":"<div><p>In this paper, we establish some new characterizations of operator monotone functions using matrix mean inequalities.\u0000</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 3-4","pages":"623 - 636"},"PeriodicalIF":0.5,"publicationDate":"2024-11-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826097","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
Béla Szőkefalvi-Nagy Medal 2024 贝拉-绍克法尔维--2024 年大奖章
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-11-25 DOI: 10.1007/s44146-024-00168-0
{"title":"Béla Szőkefalvi-Nagy Medal 2024","authors":"","doi":"10.1007/s44146-024-00168-0","DOIUrl":"10.1007/s44146-024-00168-0","url":null,"abstract":"","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 3-4","pages":"323 - 324"},"PeriodicalIF":0.5,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826204","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
Ergodic theorems for the (L^1)-Karcher mean
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-11-21 DOI: 10.1007/s44146-024-00154-6
Jorge Antezana, Eduardo Ghiglioni, Yongdo Lim, Miklós Pálfia
{"title":"Ergodic theorems for the (L^1)-Karcher mean","authors":"Jorge Antezana,&nbsp;Eduardo Ghiglioni,&nbsp;Yongdo Lim,&nbsp;Miklós Pálfia","doi":"10.1007/s44146-024-00154-6","DOIUrl":"10.1007/s44146-024-00154-6","url":null,"abstract":"<div><p>Recently the Karcher mean has been extended to the case of probability measures of positive operators on infinite-dimensional Hilbert spaces as the unique solution of a nonlinear operator equation on the convex Banach-Finsler manifold of positive operators. Let <span>((Omega ,mu ))</span> be a probability space, and let <span>(tau :Omega rightarrow Omega )</span> be a totally ergodic map. The main result of this paper is a new ergodic theorem for functions <span>( Fin L^1(Omega ,mathbb {P}))</span>, where <span>(mathbb {P})</span> is the open cone of the strictly positive operators acting on a (separable) Hilbert space. In our result, we use inductive means to average the elements of the orbit, and we prove that almost surely these averages converge to the Karcher mean of the push-forward measure <span>(F_*(mu ))</span>. From our result, we recover the strong law of large numbers and the “no dice” results proved by the third and fourth authors in the article <i>Strong law of large numbers for the</i> <span>(L^1)</span>-<i>Karcher mean</i>, Journal of Func. Anal. 279 (2020). From our main result, we also deduce an ergodic theorem for Markov chains with state space included in <span>(mathbb {P})</span>.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 3-4","pages":"575 - 591"},"PeriodicalIF":0.5,"publicationDate":"2024-11-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826433","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
Computational aspects of the geometric mean of two matrices: a survey
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-09-04 DOI: 10.1007/s44146-024-00155-5
Dario A. Bini, Bruno Iannazzo
{"title":"Computational aspects of the geometric mean of two matrices: a survey","authors":"Dario A. Bini,&nbsp;Bruno Iannazzo","doi":"10.1007/s44146-024-00155-5","DOIUrl":"10.1007/s44146-024-00155-5","url":null,"abstract":"<div><p>Algorithms for the computation of the (weighted) geometric mean <i>G</i> of two positive definite matrices are described and discussed. For large and sparse matrices the problem of computing the product <span>(y=Gb)</span>, and of solving the linear system <span>(Gx=b)</span>, without forming <i>G</i>, is addressed. An analysis of the conditioning is provided. Substantial numerical experimentation is carried out to test and compare the performances of these algorithms in terms of CPU time, numerical stability, and number of iterative steps.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 3-4","pages":"349 - 389"},"PeriodicalIF":0.5,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s44146-024-00155-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826234","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 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, Javad Mashreghi, Frédéric Morneau-Guérin","doi":"10.1007/s44146-024-00152-8","DOIUrl":"https://doi.org/10.1007/s44146-024-00152-8","url":null,"abstract":"","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"25 7","pages":""},"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}}$$ 不可逆算子 I
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-07-16 DOI: 10.1007/s44146-024-00151-9
Asma Lahmar, H. Skhiri
{"title":"$$Delta _{{{varvec{i}}}_{g}}$$-invertible operators I","authors":"Asma Lahmar, H. Skhiri","doi":"10.1007/s44146-024-00151-9","DOIUrl":"https://doi.org/10.1007/s44146-024-00151-9","url":null,"abstract":"","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"48 14","pages":""},"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
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