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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
P. Aiena, Fabio Burderi, S. Triolo
{"title":"On S-Weyl’s theorem and property (t) for some classes of operators","authors":"P. Aiena, Fabio Burderi, S. Triolo","doi":"10.1007/s44146-024-00147-5","DOIUrl":"https://doi.org/10.1007/s44146-024-00147-5","url":null,"abstract":"","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"74 19","pages":""},"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
Symmetric operator means
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
Nonlinear matrix equations involving Kubo–Ando means
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-06-20 DOI: 10.1007/s44146-024-00144-8
Trung Hoa Dinh, Anh Vu Le, Anh Thi Nguyen, Ai Nhan D. Nguyen
{"title":"Nonlinear matrix equations involving Kubo–Ando means","authors":"Trung Hoa Dinh,&nbsp;Anh Vu Le,&nbsp;Anh Thi Nguyen,&nbsp;Ai Nhan D. Nguyen","doi":"10.1007/s44146-024-00144-8","DOIUrl":"10.1007/s44146-024-00144-8","url":null,"abstract":"<div><p>In this paper, we consider two generalized matrix equations that involve an arbitrary Kubo–Ando mean. We also study the multi-step stationary iterative method for these equations and prove the corresponding convergences.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 3-4","pages":"667 - 678"},"PeriodicalIF":0.5,"publicationDate":"2024-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826287","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
Log-majorization and matrix norm inequalities with application to quantum information
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-06-14 DOI: 10.1007/s44146-024-00142-w
Fumio Hiai
{"title":"Log-majorization and matrix norm inequalities with application to quantum information","authors":"Fumio Hiai","doi":"10.1007/s44146-024-00142-w","DOIUrl":"10.1007/s44146-024-00142-w","url":null,"abstract":"<div><p>We are concerned with log-majorization for matrices in connection with the multivariate Golden–Thompson trace inequality and the Karcher mean (i.e., a multivariate extension of the weighted geometric mean). We show an extension of Araki’s log-majorization and apply it to the <span>(alpha )</span>-<i>z</i>-Rényi divergence in quantum information. We discuss the equality cases in the multivariate trace inequality of Golden–Thompson type and in the norm inequality for the Karcher mean. The paper includes an appendix to correct the proof of the author’s old result on the equality case in the norm inequality for the weighted geometric mean.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 3-4","pages":"527 - 549"},"PeriodicalIF":0.5,"publicationDate":"2024-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826289","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
Remarks on the matrix arithmetic–geometric mean inequality 关于矩阵算术几何平均数不等式的注释
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-06-13 DOI: 10.1007/s44146-024-00143-9
Rajendra Bhatia
{"title":"Remarks on the matrix arithmetic–geometric mean inequality","authors":"Rajendra Bhatia","doi":"10.1007/s44146-024-00143-9","DOIUrl":"10.1007/s44146-024-00143-9","url":null,"abstract":"<div><p>This note offers some remarks on a norm version of the matrix arithmetic–geometric inequality.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 3-4","pages":"409 - 418"},"PeriodicalIF":0.5,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141346714","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
Correction to: Derivable maps at commutative products on Banach algebras 更正：巴拿赫代数上交换积的可派生映射
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-06-03 DOI: 10.1007/s44146-024-00138-6
Abbas Zivari-Kazempour, H. Ghahramani, Wu Jing
{"title":"Correction to: Derivable maps at commutative products on Banach algebras","authors":"Abbas Zivari-Kazempour, H. Ghahramani, Wu Jing","doi":"10.1007/s44146-024-00138-6","DOIUrl":"https://doi.org/10.1007/s44146-024-00138-6","url":null,"abstract":"","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"118 12","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141272145","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
J-selfadjoint matrix means and their indefinite inequalities J 自交矩阵手段及其不定不等式
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-05-29 DOI: 10.1007/s44146-024-00136-8
N. Bebiano, R. Lemos, G. Soares
{"title":"J-selfadjoint matrix means and their indefinite inequalities","authors":"N. Bebiano,&nbsp;R. Lemos,&nbsp;G. Soares","doi":"10.1007/s44146-024-00136-8","DOIUrl":"10.1007/s44146-024-00136-8","url":null,"abstract":"<div><p>Let <i>J</i> be a non trivial involutive Hermitian matrix. Consider <span>({mathbb {C}}^n)</span> equipped with the indefinite inner product induced by <i>J</i>, <span>([x,y]=y^*J x)</span> for all <span>(x,yin {{mathbb {C}}}^n,)</span> which endows the matrix algebra <span>({mathbb {C}}^{ntimes n})</span> with a partial order relation <span>(le ^J)</span> between <i>J</i>-selfadjoint matrices. Inde-finite inequalities are given in this setup, involving the <i>J</i>-selfadjoint <span>(alpha )</span>-weighted geometric matrix mean. In particular, an indefinite version of Ando–Hiai inequality is proved to be equivalent to Furuta inequality of indefinite type.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 3-4","pages":"513 - 525"},"PeriodicalIF":0.5,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s44146-024-00136-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826329","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
Extended power difference means 扩展功率差意味着
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-05-20 DOI: 10.1007/s44146-024-00137-7
Shuhei Wada
{"title":"Extended power difference means","authors":"Shuhei Wada","doi":"10.1007/s44146-024-00137-7","DOIUrl":"10.1007/s44146-024-00137-7","url":null,"abstract":"<div><p>The extended power difference mean <span>(f_{a,b}(t):={bover a}{{t^a-1}over {t^b-1}})</span> <span>((a,bin {mathbb {R}}))</span> is investigated in this paper. We show some Thompson metric inequalities involving <span>(f_{a,b})</span> and Tsallis relative operator entropy. We also discuss the behavior of the bivariate function defined as the perspective map for <span>(f_{a,b})</span>. Finally, the relationship beween <span>(f_{a,b})</span> and the weighted logarithmic mean is studied.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"90 3-4","pages":"491 - 512"},"PeriodicalIF":0.5,"publicationDate":"2024-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141120835","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
Some unitary similarity invariant functional values preservers of matrix products 矩阵乘积的一些单元相似不变函数值保持器
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-05-18 DOI: 10.1007/s44146-024-00134-w
M. Bendaoud, A. Benyouness
{"title":"Some unitary similarity invariant functional values preservers of matrix products","authors":"M. Bendaoud, A. Benyouness","doi":"10.1007/s44146-024-00134-w","DOIUrl":"https://doi.org/10.1007/s44146-024-00134-w","url":null,"abstract":"","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"111 31","pages":""},"PeriodicalIF":0.5,"publicationDate":"2024-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141125916","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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