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dc.contributor.authorMarcoux, Laurent W.
dc.contributor.authorPopov, Alexey I.
dc.date.accessioned2020-04-01 21:34:08 (GMT)
dc.date.available2020-04-01 21:34:08 (GMT)
dc.descriptionOriginally published by Duke University Pressen
dc.description.abstractSuppose 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 𝒜⊆ℬ(H) is an abelian algebra with the property that given any bounded representation ϱ:𝒜→ℬ(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.en
dc.description.sponsorshipNatural Sciences and Engineering Research Council (NSERC)en
dc.publisherDuke University Pressen
dc.subjectabelian operatoren
dc.subjectBanach algebraen
dc.subjecttotal reduction propertyen
dc.titleAbelian, amenable operator algebras are similar to C∗ -algebrasen
dcterms.bibliographicCitationMarcoux, Laurent W.; Popov, Alexey I. Abelian, amenable operator algebras are similar to $C^{*}$ -algebras. Duke Math. J. 165 (2016), no. 12, 2391--2406. doi:10.1215/00127094-3619791. https://projecteuclid.org/euclid.dmj/1473186403en
uws.contributor.affiliation1Faculty of Mathematicsen
uws.contributor.affiliation2Pure Mathematicsen

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