Abelian, amenable operator algebras are similar to C∗ -algebras
| dc.contributor.author | Marcoux, Laurent W. | |
| dc.contributor.author | Popov, Alexey I. | |
| dc.date.accessioned | 2020-04-01T21:34:08Z | |
| dc.date.available | 2020-04-01T21:34:08Z | |
| dc.date.issued | 2016-12 | |
| dc.description | Originally published by Duke University Press | en |
| dc.description.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 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.sponsorship | Natural Sciences and Engineering Research Council (NSERC) | en |
| dc.identifier.uri | https://doi.org/10.1215/00127094-3619791 | |
| dc.identifier.uri | http://hdl.handle.net/10012/15731 | |
| dc.language.iso | en | en |
| dc.publisher | Duke University Press | en |
| dc.subject | abelian operator | en |
| dc.subject | Banach algebra | en |
| dc.subject | C∗-algebra | en |
| dc.subject | total reduction property | en |
| dc.title | Abelian, amenable operator algebras are similar to C∗ -algebras | en |
| dc.type | Article | en |
| dcterms.bibliographicCitation | Marcoux, 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/1473186403 | en |
| uws.contributor.affiliation1 | Faculty of Mathematics | en |
| uws.contributor.affiliation2 | Pure Mathematics | en |
| uws.peerReviewStatus | Reviewed | en |
| uws.scholarLevel | Faculty | en |
| uws.scholarLevel | Graduate | en |
| uws.typeOfResource | Text | en |