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Published online by Cambridge University Press:  11 March 2010

Institut für Analysis, Karlsruhe Institute of Technology, Kaiserstrasse 89, 76133 Karlsruhe, Germany Laboratoire de Mathématiques, Université de Franche-Comté, 25030 Besançon Cedex, France (email:
Laboratoire de Mathématiques, Université de Franche-Comté, 25030 Besançon Cedex, France (email:
For correspondence; e-mail:
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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.

MSC classification

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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