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Nonlinear matrix equations involving Kubo–Ando means 涉及久保-安藤均值的非线性矩阵方程
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 对数最大化和矩阵范数不等式在量子信息中的应用
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, Hoger Ghahramani, Wu Jing
{"title":"Correction to: Derivable maps at commutative products on Banach algebras","authors":"Abbas Zivari-Kazempour,&nbsp;Hoger Ghahramani,&nbsp;Wu Jing","doi":"10.1007/s44146-024-00138-6","DOIUrl":"10.1007/s44146-024-00138-6","url":null,"abstract":"","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"91 1-2","pages":"337 - 337"},"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
Non-linear characterization of Jordan (*)-isomorphisms via maps on positive cones of (C^*)-algebras (C^*) -代数正锥上映射的Jordan (*) -同构的非线性表征
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-05-27 DOI: 10.1007/s44146-024-00140-y
Osamu Hatori, Shiho Oi
{"title":"Non-linear characterization of Jordan (*)-isomorphisms via maps on positive cones of (C^*)-algebras","authors":"Osamu Hatori,&nbsp;Shiho Oi","doi":"10.1007/s44146-024-00140-y","DOIUrl":"10.1007/s44146-024-00140-y","url":null,"abstract":"<div><p>We study maps between positive definite or positive semidefinite cones of unital <span>(C^*)</span>-algebras. We describe surjective maps that preserve </p><ol>\u0000 <li>\u0000 <span>(1)</span>\u0000 \u0000 <p>the norm of the quotient or product of elements;</p>\u0000 \u0000 </li>\u0000 <li>\u0000 <span>(2)</span>\u0000 \u0000 <p>the spectrum of the quotient or product of elements;</p>\u0000 \u0000 </li>\u0000 <li>\u0000 <span>(3)</span>\u0000 \u0000 <p>the spectral seminorm of the quotient or product of elements.</p>\u0000 \u0000 </li>\u0000 </ol><p> These maps relate to the Jordan <span>(*)</span>-isomorphisms between the specified <span>(C^*)</span>-algebras. While a surjection between positive definite cones that preserves the norm of the quotient of elements may not be extended to a linear map between the underlying <span>(C^*)</span>-algebras, the other types of surjections can be extended to a Jordan <span>(*)</span>-isomorphism or a Jordan <span>(*)</span>-isomorphism followed by 2-sided multiplication by a positive invertible element. We also study conditions for the centrality of positive invertible elements. We generalize “the corollary” regarding surjections between positive semidefinite cones of unital <span>(C^*)</span>-algebras. Applying it, we provide positive solutions to the problem posed by Molnár for general unital <span>(C^*)</span>-algebras.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"91 1-2","pages":"313 - 336"},"PeriodicalIF":0.5,"publicationDate":"2024-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143938692","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 some large filters of quasiorder lattices 生成一些大的拟序格滤波器
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-05-25 DOI: 10.1007/s44146-024-00139-5
Gábor Czédli
{"title":"Generating some large filters of quasiorder lattices","authors":"Gábor Czédli","doi":"10.1007/s44146-024-00139-5","DOIUrl":"10.1007/s44146-024-00139-5","url":null,"abstract":"<div><p>For a poset <span>((P;le ))</span>, the quasiorders (AKA preorders) extending the poset order “<span>(le )</span>” form a complete lattice <i>F</i>, which is a filter in the lattice of all quasiorders of the set <i>P</i>. We prove that if the poset order “<span>(le )</span>” is small, then <i>F</i> can be generated by few elements.</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"91 1-2","pages":"1 - 21"},"PeriodicalIF":0.5,"publicationDate":"2024-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143938507","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
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,&nbsp;A. Benyouness","doi":"10.1007/s44146-024-00134-w","DOIUrl":"10.1007/s44146-024-00134-w","url":null,"abstract":"<div><p>Let <span>({mathcal {M}}_{n})</span> be the algebra of <span>(ntimes n)</span> complex matrices. Complete descriptions are given of the maps on <span>({mathcal {M}}_{n})</span> leaving invariant some unitary similarity invariant functional values of the product of matrices such as the numerical radius, the pseudo spectral radius, or the condition spectral radius.\u0000</p></div>","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"91 1-2","pages":"247 - 265"},"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
Correction to: Fixed point and periodic point theorems 修正:不动点定理和周期点定理
IF 0.5
ACTA SCIENTIARUM MATHEMATICARUM Pub Date : 2024-05-16 DOI: 10.1007/s44146-024-00135-9
R. P. Pant, Vladimir Rakočević
{"title":"Correction to: Fixed point and periodic point theorems","authors":"R. P. Pant,&nbsp;Vladimir Rakočević","doi":"10.1007/s44146-024-00135-9","DOIUrl":"10.1007/s44146-024-00135-9","url":null,"abstract":"","PeriodicalId":46939,"journal":{"name":"ACTA SCIENTIARUM MATHEMATICARUM","volume":"91 1-2","pages":"339 - 339"},"PeriodicalIF":0.5,"publicationDate":"2024-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143938585","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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