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, Anh Vu Le, Anh Thi Nguyen, 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}
{"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}
{"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}
{"title":"Correction to: Derivable maps at commutative products on Banach algebras","authors":"Abbas Zivari-Kazempour, Hoger Ghahramani, 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}
{"title":"J-selfadjoint matrix means and their indefinite inequalities","authors":"N. Bebiano, R. Lemos, 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}
{"title":"Non-linear characterization of Jordan (*)-isomorphisms via maps on positive cones of (C^*)-algebras","authors":"Osamu Hatori, 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}
{"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}
{"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}
{"title":"Some unitary similarity invariant functional values preservers of matrix products","authors":"M. Bendaoud, 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}
{"title":"Correction to: Fixed point and periodic point theorems","authors":"R. P. Pant, 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}