Operator synthesis. I. Synthetic sets, bilattices and tensor algebras |
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Authors: | Victor Shulman |
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Institution: | a Vologda State Liceum of Mathematical and Natural Sciences, Vologda, 160000, Russia b Department of Mathematics, Chalmers University of Technology, SE-412 96 Göteborg, Sweden |
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Abstract: | The interplay between the invariant subspace theory and spectral synthesis for locally compact abelian group discovered by Arveson (Ann. of Math. (2) 100 (1974) 433) 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 Arveson. We solve some problems posed in Arveson (1974). |
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Keywords: | Bilattice Bimodule Operator synthesis Spectral synthesis Tensor algebras |
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