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Abstract: Let K be any compact set. The C^*-algebra CK is nuclear and any boundedhomomorphism from CK into BH, the algebra of all bounded operators on someHilbert space H, is automatically completely bounded. We prove extensions ofthese results to the Banach space setting, using the key concept ofR-boundedness. Then we apply these results to operators with a uniformlybounded H^\infty-calculus, as well as to unconditionality on L^p. We show thatany unconditional basis on L^p `is- an unconditional basis on L^2 after anappropriate change of density.



Author: Christoph Kriegler, Christian Le Merdy

Source: https://arxiv.org/







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