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1 September 2016 Abelian, amenable operator algebras are similar to C-algebras
Laurent W. Marcoux, Alexey I. Popov
Duke Math. J. 165(12): 2391-2406 (1 September 2016). DOI: 10.1215/00127094-3619791

Abstract

Suppose that H is a complex Hilbert space and that B(H) denotes the bounded linear operators on H. We show that every abelian, amenable operator algebra is similar to a C-algebra. We do this by showing that if AB(H) is an abelian algebra with the property that given any bounded representation ϱ:AB(Hϱ) of A on a Hilbert space Hϱ, every invariant subspace of ϱ(A) is topologically complemented by another invariant subspace of ϱ(A), then A is similar to an abelian C-algebra.

Citation

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Laurent W. Marcoux. Alexey I. Popov. "Abelian, amenable operator algebras are similar to C-algebras." Duke Math. J. 165 (12) 2391 - 2406, 1 September 2016. https://doi.org/10.1215/00127094-3619791

Information

Received: 6 April 2015; Revised: 7 October 2015; Published: 1 September 2016
First available in Project Euclid: 6 September 2016

zbMATH: 1362.46048
MathSciNet: MR3544284
Digital Object Identifier: 10.1215/00127094-3619791

Subjects:
Primary: 46J05
Secondary: 47L10, 47L30

Rights: Copyright © 2016 Duke University Press

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Vol.165 • No. 12 • 1 September 2016
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