Finitely correlated representations of product systems of -correspondences over
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| Title: | Finitely correlated representations of product systems of -correspondences over |
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| Authors: | Fuller, Adam Hanley1 a2fuller@math.uwaterloo.ca |
| Source: | Journal of Functional Analysis. Jan2011, Vol. 260 Issue 2, p574-611. 38p. |
| Subjects: | Finite fields, Statistical correlation, Graph theory, Algebra, Isometrics (Mathematics), Semigroups (Algebra), Dilation theory (Operator theory) |
| Abstract: | Abstract: We study isometric representations of product systems of correspondences over the semigroup which are minimal dilations of finite-dimensional, fully coisometric representations. We show the existence of a unique minimal cyclic coinvariant subspace for all such representations. The compression of the representation to this subspace is shown to be a complete unitary invariant. For a certain class of graph algebras the nonself-adjoint wot-closed algebra generated by these representations is shown to contain the projection onto the minimal cyclic coinvariant subspace. This class includes free semigroup algebras. This result extends to a class of higher-rank graph algebras which includes higher-rank graphs with a single vertex. [ABSTRACT FROM AUTHOR] |
| 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 |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 54886221 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Finitely correlated representations of product systems of -correspondences over – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Fuller%2C+Adam+Hanley%22">Fuller, Adam Hanley</searchLink><relatesTo>1</relatesTo><i> a2fuller@math.uwaterloo.ca</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Functional+Analysis%22">Journal of Functional Analysis</searchLink>. Jan2011, Vol. 260 Issue 2, p574-611. 38p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Finite+fields%22">Finite fields</searchLink><br /><searchLink fieldCode="DE" term="%22Statistical+correlation%22">Statistical correlation</searchLink><br /><searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Isometrics+%28Mathematics%29%22">Isometrics (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Semigroups+%28Algebra%29%22">Semigroups (Algebra)</searchLink><br /><searchLink fieldCode="DE" term="%22Dilation+theory+%28Operator+theory%29%22">Dilation theory (Operator theory)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Abstract: We study isometric representations of product systems of correspondences over the semigroup which are minimal dilations of finite-dimensional, fully coisometric representations. We show the existence of a unique minimal cyclic coinvariant subspace for all such representations. The compression of the representation to this subspace is shown to be a complete unitary invariant. For a certain class of graph algebras the nonself-adjoint wot-closed algebra generated by these representations is shown to contain the projection onto the minimal cyclic coinvariant subspace. This class includes free semigroup algebras. This result extends to a class of higher-rank graph algebras which includes higher-rank graphs with a single vertex. [ABSTRACT FROM AUTHOR] – 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.2010.10.004 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 38 StartPage: 574 Subjects: – SubjectFull: Finite fields Type: general – SubjectFull: Statistical correlation Type: general – SubjectFull: Graph theory Type: general – SubjectFull: Algebra Type: general – SubjectFull: Isometrics (Mathematics) Type: general – SubjectFull: Semigroups (Algebra) Type: general – SubjectFull: Dilation theory (Operator theory) Type: general Titles: – TitleFull: Finitely correlated representations of product systems of -correspondences over Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Fuller, Adam Hanley IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 01 Text: Jan2011 Type: published Y: 2011 Identifiers: – Type: issn-print Value: 00221236 Numbering: – Type: volume Value: 260 – Type: issue Value: 2 Titles: – TitleFull: Journal of Functional Analysis Type: main |
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