TENSOR EXTENSION PROPERTIES OF C(K)-REPRESENTATIONS AND APPLICATIONS TO UNCONDITIONALITY
Published online by Cambridge University Press: 11 March 2010
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 ofR-boundedness. Then we apply these results to operators with a uniformly bounded H∞-calculus, as well as to unconditionality on Lp. We show that any unconditional basis on Lp ‘is’ an unconditional basis on L2 after an appropriate change of density.
- Research Article
- Copyright © Australian Mathematical Publishing Association Inc. 2010
The first author is supported by the Karlsruhe House of Young Scientists and the Franco-German University DFH-UFA, the second author is supported by the research program ANR-06-BLAN-0015.
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