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

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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.
32 pages. to appear in Journal of Functional Analysis

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Functional Analysis, Operator Algebras, 47D15 (Primary), 47D25, 43A45, 43A46 (Secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/68384

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0308240
 http://arxiv.org/abs/math/0308240

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arXiv