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

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

2003-08-26

arxiv.org/abs/math/0308240v1

Mathematics

Functional Analysis

32 pages. to appear in Journal of Functional Analysis

Scientific paper

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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