This is an announcement for the paper "Tensor extension properties of C(K)-representations and applications to unconditionality" by Christoph Kriegler and Christian Le Merdy.

Abstract: Let K be any compact set. The C^*-algebra C(K) is nuclear and any bounded homomorphism from C(K) into B(H), the algebra of all bounded operators on some Hilbert space H, is automatically completely bounded. We prove extensions of these results to the Banach space setting, using the key concept of R-boundedness. Then we apply these results to operators with a uniformly bounded H^\infty-calculus, as well as to unconditionality on L^p. We show that any unconditional basis on L^p `is' an unconditional basis on L^2 after an appropriate change of density.

Archive classification: math.OA math.FA

Mathematics Subject Classification: 47A60; 46B28

The source file(s), CK-Art.tex: 73146 bytes, is(are) stored in gzipped form as 0901.1025.gz with size 22kb. The corresponding postcript file has gzipped size 145kb.

Submitted from: clemerdy@univ-fcomte.fr

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