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TENSOR EXTENSION PROPERTIES OF C(K)-REPRESENTATIONS AND APPLICATIONS TO UNCONDITIONALITY

Part of: General theory of linear operators

Published online by Cambridge University Press:  11 March 2010

CHRISTOPH KRIEGLER  and
CHRISTIAN LE MERDY
CHRISTOPH KRIEGLER
Affiliation:
Institut für Analysis, Karlsruhe Institute of Technology, Kaiserstrasse 89, 76133 Karlsruhe, Germany Laboratoire de Mathématiques, Université de Franche-Comté, 25030 Besançon Cedex, France (email: [email protected])
CHRISTIAN LE MERDY*
Affiliation:
Laboratoire de Mathématiques, Université de Franche-Comté, 25030 Besançon Cedex, France (email: [email protected])
*
✉For correspondence; e-mail: [email protected]
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Abstract

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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.

Keywords

functional calculusR-boundednessunconditionalitytensor products

MSC classification

Secondary: 47A60: Functional calculus
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 88 , Issue 2 , April 2010 , pp. 205 - 230
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

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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