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Abelian, amenable operator algebras are similar to Cāˆ— -algebras

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MP20151007.pdf (299.01 KB)

Date

2016-12

Authors

Marcoux, Laurent W.
Popov, Alexey I.

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Volume Title

Publisher

Duke University Press

Abstract

Suppose that H is a complex Hilbert space and that ā„¬(H) denotes the bounded linear operators on H. We show that every abelian, amenable operator algebra is similar to a Cāˆ—-algebra. We do this by showing that if š’œāŠ†ā„¬(H) is an abelian algebra with the property that given any bounded representation Ļ±:š’œā†’ā„¬(HĻ±) of š’œ on a Hilbert space HĻ±, every invariant subspace of Ļ±(š’œ) is topologically complemented by another invariant subspace of Ļ±(š’œ), then š’œ is similar to an abelian Cāˆ—-algebra.

Description

Originally published by Duke University Press

Keywords

abelian operator, Banach algebra, Cāˆ—-algebra, total reduction property

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Citation

URI

https://doi.org/10.1215/00127094-3619791
 http://hdl.handle.net/10012/15731

Collections

Waterloo Research
Pure Mathematics