Operator algebras and subproduct systems arising from stochastic matrices.
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| Title: | Operator algebras and subproduct systems arising from stochastic matrices. |
|---|---|
| Authors: | Dor-On, Adam1 adamd@math.bgu.ac.il, Markiewicz, Daniel1 danielm@math.bgu.ac.il |
| Source: | Journal of Functional Analysis. Aug2014, Vol. 267 Issue 4, p1057-1120. 64p. |
| Subjects: | Operator algebras, Stochastic matrices, Adjoint operators (Quantum mechanics), Isomorphism (Mathematics), Automorphisms, Mathematical proofs |
| Abstract: | Abstract: We study subproduct systems in the sense of Shalit and Solel arising from stochastic matrices on countable state spaces, and their associated operator algebras. We focus on the non-self-adjoint tensor algebra, and Viselter's generalization of the Cuntz–Pimsner C*-algebra to the context of subproduct systems. Suppose that X and Y are Arveson–Stinespring subproduct systems associated to two stochastic matrices over a countable set Ω, and let and be their tensor algebras. We show that every algebraic isomorphism from onto is automatically bounded. Furthermore, and are isometrically isomorphic if and only if X and Y are unitarily isomorphic up to a *-automorphism of . When Ω is finite, we prove that and are algebraically isomorphic if and only if there exists a similarity between X and Y up to a *-automorphism of . Moreover, we provide an explicit description of the Cuntz–Pimsner algebra in the case where Ω is finite and the stochastic matrix is essential. [Copyright &y& Elsevier] |
| Copyright of Journal of Functional Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 96573891 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Operator algebras and subproduct systems arising from stochastic matrices. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Dor-On%2C+Adam%22">Dor-On, Adam</searchLink><relatesTo>1</relatesTo><i> adamd@math.bgu.ac.il</i><br /><searchLink fieldCode="AR" term="%22Markiewicz%2C+Daniel%22">Markiewicz, Daniel</searchLink><relatesTo>1</relatesTo><i> danielm@math.bgu.ac.il</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Functional+Analysis%22">Journal of Functional Analysis</searchLink>. Aug2014, Vol. 267 Issue 4, p1057-1120. 64p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Operator+algebras%22">Operator algebras</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+matrices%22">Stochastic matrices</searchLink><br /><searchLink fieldCode="DE" term="%22Adjoint+operators+%28Quantum+mechanics%29%22">Adjoint operators (Quantum mechanics)</searchLink><br /><searchLink fieldCode="DE" term="%22Isomorphism+%28Mathematics%29%22">Isomorphism (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Automorphisms%22">Automorphisms</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+proofs%22">Mathematical proofs</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Abstract: We study subproduct systems in the sense of Shalit and Solel arising from stochastic matrices on countable state spaces, and their associated operator algebras. We focus on the non-self-adjoint tensor algebra, and Viselter's generalization of the Cuntz–Pimsner C*-algebra to the context of subproduct systems. Suppose that X and Y are Arveson–Stinespring subproduct systems associated to two stochastic matrices over a countable set Ω, and let and be their tensor algebras. We show that every algebraic isomorphism from onto is automatically bounded. Furthermore, and are isometrically isomorphic if and only if X and Y are unitarily isomorphic up to a *-automorphism of . When Ω is finite, we prove that and are algebraically isomorphic if and only if there exists a similarity between X and Y up to a *-automorphism of . Moreover, we provide an explicit description of the Cuntz–Pimsner algebra in the case where Ω is finite and the stochastic matrix is essential. [Copyright &y& Elsevier] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Functional Analysis is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.jfa.2014.05.004 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 64 StartPage: 1057 Subjects: – SubjectFull: Operator algebras Type: general – SubjectFull: Stochastic matrices Type: general – SubjectFull: Adjoint operators (Quantum mechanics) Type: general – SubjectFull: Isomorphism (Mathematics) Type: general – SubjectFull: Automorphisms Type: general – SubjectFull: Mathematical proofs Type: general Titles: – TitleFull: Operator algebras and subproduct systems arising from stochastic matrices. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Dor-On, Adam – PersonEntity: Name: NameFull: Markiewicz, Daniel IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 08 Text: Aug2014 Type: published Y: 2014 Identifiers: – Type: issn-print Value: 00221236 Numbering: – Type: volume Value: 267 – Type: issue Value: 4 Titles: – TitleFull: Journal of Functional Analysis Type: main |
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