Operator synthesis. I. Synthetic sets, bilattices and tensor algebras

2003/08/26 by Victor Shulman, Shulman, Victor, Lyudmila Turowska +1
Mathematics · #43A45 #43A46 (Secondary) #47D15 (Primary) #47D25 #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #math.FA #math.OA #msc:43A45 #msc:43A46 #msc:47D15 #msc:47D25

paper · pdf · doi:10.48550/arxiv.math/0308240

32 pages. to appear in Journal of Functional Analysis

arxiv created 2003/08/26 · arxiv updated 2009/12/01

Abstract

The interplay between the invariant subspace theory and spectral synthesis for locally compact abelian group discovered by Arveson is extended to include other topics as harmonic analysis for Varopoulos algebras and approximation by projection-valued measures. We propose a ''coordinate'' approach which nevertheless does not use the technique of pseudo-integral operators, as well as a coordinate free one which allows to extend to non-separable spaces some important results and constructions of [W.Arveson, Operator Alegebras and Invariant subspaces, Ann. of Math. (2) 100 (1974)] and solve some problems posed there.

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