{"title":"On dynamics of quantum states generated by averaging of random shifts","authors":"Grigori Amosov, Vsevolod Sakbaev","doi":"10.1007/s43036-025-00440-2","DOIUrl":"10.1007/s43036-025-00440-2","url":null,"abstract":"<div><p>Quantum channels are usually studied as the completely positive trace preserving linear mapping of the space of normal quantum states into itself. We study the extension of an above quantum channel to the space of quantum states of general type that are convex combinations of normal states and singular states according to the Yosida–Hewitt decomposition. The interest to the study of quantum dynamics on the set of general quantum states arises in the consideration of a quantum dynamical semigroup acting in a Hilbert space of functions of infinite dimensional argument. In this case the above semigroup maps any pure vector quantum state into a state of general type. This effect can be considered in the example of averaging of quantum dynamical semigroup generated by a shift argument on a random Gaussian vector.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 3","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143875465","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":"Characterization of the existence of an (L)-(U) factorization","authors":"Charles R. Johnson, Pavel Okunev","doi":"10.1007/s43036-024-00400-2","DOIUrl":"10.1007/s43036-024-00400-2","url":null,"abstract":"<div><p>For the first time, a characterization is given of the circumstances under which an <i>n</i>-by-<i>n</i> matrix over a field has an <span>(L)</span>-<span>(U)</span> factorization. This is in terms of a comparison of ranks of the leading <i>k</i>-by-<i>k</i> principal submatrix to the rank of the first <i>k</i> columns and first <i>k</i> rows. Known results about special types of <span>(L)</span>-<span>(U)</span> factorizations follow as do some new results about near <span>(L)</span>-<span>(U)</span> factorization when a conventional <span>(L)</span>-<span>(U)</span> factorization does not exist. The proof allows explicit construction of an <span>(L)</span>-<span>(U)</span> factorization when one exists.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143840488","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":"Sampling recovery of functions with mixed smoothness","authors":"E. D. Kosov, V. N. Temlyakov","doi":"10.1007/s43036-025-00439-9","DOIUrl":"10.1007/s43036-025-00439-9","url":null,"abstract":"<div><p>Recently, a substantial progress in studying the problem of optimal sampling recovery was made in a number of papers. In particular, this resulted in some progress in studying sampling recovery on function classes with mixed smoothness. Mostly, the case of recovery in the square norm was studied. In this paper we combine some of the new ideas developed recently in order to obtain progress in sampling recovery on classes with mixed smoothness in other integral norms.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143824588","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":"A note on (L^p)-(L^q) boundedness of Fourier multipliers on noncommutative spaces","authors":"Michael Ruzhansky, Kanat Tulenov","doi":"10.1007/s43036-025-00436-y","DOIUrl":"10.1007/s43036-025-00436-y","url":null,"abstract":"<div><p>In this work, we study Fourier multipliers on noncommutative spaces. In particular, we show a simple proof of <span>(L^p)</span>-<span>(L^q)</span> estimate of Fourier multipliers on general noncommutative spaces associated with semifinite von Neumann algebras. This includes the case of Fourier multipliers on general locally compact unimodular groups.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00436-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143793267","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":"Approximate Roberts directional orthogonalities","authors":"Kallal Pal, Sumit Chandok","doi":"10.1007/s43036-025-00433-1","DOIUrl":"10.1007/s43036-025-00433-1","url":null,"abstract":"<div><p>We define two types of approximate Roberts orthogonality with direction in the framework of a complex normed space. We examine their geometrical properties and demonstrate that the notion of <span>(epsilon )</span>-approximate directional orthogonality is weaker than that of <span>(epsilon )</span>-approximate orthogonality. Concerning the approximate Birkhoff orthogonality, we talk about the connection between them. Also, we provide the notion of an approximation Roberts directional orthogonality set and analyze the geometric characteristics of these sets. Furthermore, we discuss approximate orthogonality preserving mapping.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143735427","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":"New estimates for numerical radius in (C^*)-algebras","authors":"Ali Zamani","doi":"10.1007/s43036-025-00434-0","DOIUrl":"10.1007/s43036-025-00434-0","url":null,"abstract":"<div><p>Several numerical radius inequalities in the framework of <span>(C^*)</span>-algebras are proved in this paper. These results, which are based on an extension of the Buzano inequality for elements in a pre-Hilbert <span>(C^*)</span>-module, generalize earlier numerical radius inequalities. An expression for the <span>(C^*)</span>-algebra-valued norm based on the numerical radius is also given.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143698486","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 non-homogeneous Cauchy problems with time-dependent generators","authors":"Pedro Marín-Rubio, Paulo N. Seminario-Huertas","doi":"10.1007/s43036-025-00435-z","DOIUrl":"10.1007/s43036-025-00435-z","url":null,"abstract":"<div><p>In this paper it is studied the well-posedness in several senses for non-homogeneous Cauchy problems where the infinitesimal generator depends on the time parameter. More specifically, we analyze the existence of classical, mild and weak solutions and their relationships. Thanks to uniqueness arguments, mild solutions are proved to satisfy a classical variational formulation. Finally, these results are applied to a thermoelastic plate model where the thermal part is of Cattaneo type and all the physical coefficients depend on time.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00435-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143688269","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":"Inequalities among the nth residual relative operator entropies","authors":"Hiroaki Tohyama, Eizaburo Kamei, Masayuki Watanabe","doi":"10.1007/s43036-025-00431-3","DOIUrl":"10.1007/s43036-025-00431-3","url":null,"abstract":"<div><p>We showed two types of operator inequalities between the <span>((n+1))</span>th residual relative operator entropy and the difference of the <i>n</i>th residual relative operator entropies. They are similar partially but have some differences. We investigate what these differences come from. Inequalities other than the previous ones are given through this process.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143676478","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":"An approach to root functions of matrix polynomials with applications in differential equations and meromorphic matrix functions","authors":"Muhamed Borogovac","doi":"10.1007/s43036-025-00432-2","DOIUrl":"10.1007/s43036-025-00432-2","url":null,"abstract":"<div><p>First, we present a method for obtaining a canonical set of root functions and Jordan chains of the invertible matrix polynomial <i>L</i>(<i>z</i>) through elementary transformations of the matrix <i>L</i>(<i>z</i>) alone. This method provides a new and simple approach to deriving a general solution of the system of ordinary linear differential equations <span>(Lleft( frac{d}{dt}right) u=0)</span>, where <i>u</i>(<i>t</i>) is <i>n</i>-dimensional unknown function. We illustrate the effectiveness of this method by applying it to solve a high-order linear system of ODEs. Second, given a matrix generalized Nevanlinna function <span>(Qin N_{kappa }^{n times n})</span>, that satisfies certain conditions at <span>(infty )</span>, and a canonical set of root functions of <span>(hat{Q}(z):= -Q(z)^{-1})</span>, we construct the corresponding Pontryagin space <span>((mathcal {K}, [.,.]))</span>, a self-adjoint operator <span>(A:mathcal {K}rightarrow mathcal {K})</span>, and an operator <span>(Gamma : mathbb {C}^{n}rightarrow mathcal {K})</span>, that represent the function <i>Q</i>(<i>z</i>) in a Krein–Langer type representation. We illustrate the application of main results with examples involving concrete matrix polynomials <i>L</i>(<i>z</i>) and their inverses, defined as <span>(Q(z):=hat{L}(z):= -L(z)^{-1})</span>.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s43036-025-00432-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143668363","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":"2-Local automorphisms and derivations of triangular matrices","authors":"Wenbo Huang, Shan Li","doi":"10.1007/s43036-025-00430-4","DOIUrl":"10.1007/s43036-025-00430-4","url":null,"abstract":"<div><p>Let <span>(mathcal {T})</span> denote the algebra of all <span>(2 times 2)</span> upper triangular matrices over a field <span>(mathbb {F})</span>. We show that the linear space of all 2-local derivations on <span>(mathcal {T})</span> decomposes as <span>(mathcal {L} = mathcal {D} oplus mathcal {L}_0)</span>, where <span>(mathcal {D})</span> is the subspace of all derivations, and <span>(mathcal {L}_0)</span> consists of 2-local derivations vanishing on a subset of <span>(mathcal {T})</span>, isomorphic to the space of functions <span>(f:mathbb {F}rightarrow mathbb {F})</span> such that <span>(f(0)=0)</span>. For any 2-local automorphism <span>(Lambda )</span> on <span>(mathcal {T})</span>, we show that there exists a unique automorphism <span>(phi )</span> and a 2-local automorphism <span>(Lambda _{1} in varPsi )</span> such that <span>(Lambda = phi Lambda _1)</span>, where <span>(varPsi )</span> is the monoid of 2-local automorphisms that act as the identity on a subset of <span>(mathcal {T})</span>. Furthermore, we establish that <span>(varPsi )</span> is isomorphic to the monoid of injective functions from <span>(mathbb {F}^{*})</span> to itself.</p></div>","PeriodicalId":44371,"journal":{"name":"Advances in Operator Theory","volume":"10 2","pages":""},"PeriodicalIF":0.8,"publicationDate":"2025-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638424","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}
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