Operator *-correspondences in analysis and geometry

David Blecher, Jens Kaad, Bram Mesland

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Resumé

An operator *-algebra is a non-self-adjoint operator algebra with completely isometric involution. We show that any operator *-algebra admits a faithful representation on a Hilbert space in such a way that the involution coincides with the operator adjoint up to conjugation by a symmetry. We introduce operator *-correspondences as a general class of inner product modules over operator *-algebras and prove a similar representation theorem for them. From this, we derive the existence of linking operator (Fo -algebras for operator * -correspondences. We illustrate the relevance of this class of inner product modules by providing numerous examples arising from noncommutative geometry.

OriginalsprogEngelsk
TidsskriftProceedings of the London Mathematical Society
Vol/bind117
Udgave nummer2
Sider (fra-til)303-344
ISSN0024-6115
DOI
StatusUdgivet - 2018

Fingeraftryk

Operator Algebras
Correspondence
Operator
Scalar, inner or dot product
Involution
Adjoint Operator
Module
Non-self-adjoint Operator
Noncommutative Geometry
Representation Theorem
Conjugation
Faithful
Isometric
Linking
Hilbert space
Symmetry
Class

Citer dette

Blecher, David ; Kaad, Jens ; Mesland, Bram. / Operator *-correspondences in analysis and geometry. I: Proceedings of the London Mathematical Society. 2018 ; Bind 117, Nr. 2. s. 303-344.
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Operator *-correspondences in analysis and geometry. / Blecher, David; Kaad, Jens; Mesland, Bram.

I: Proceedings of the London Mathematical Society, Bind 117, Nr. 2, 2018, s. 303-344.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningpeer review

TY - JOUR

T1 - Operator *-correspondences in analysis and geometry

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AU - Kaad, Jens

AU - Mesland, Bram

PY - 2018

Y1 - 2018

N2 - An operator *-algebra is a non-self-adjoint operator algebra with completely isometric involution. We show that any operator *-algebra admits a faithful representation on a Hilbert space in such a way that the involution coincides with the operator adjoint up to conjugation by a symmetry. We introduce operator *-correspondences as a general class of inner product modules over operator *-algebras and prove a similar representation theorem for them. From this, we derive the existence of linking operator (Fo -algebras for operator * -correspondences. We illustrate the relevance of this class of inner product modules by providing numerous examples arising from noncommutative geometry.

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