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Journal of the London Mathematical Society Advance Access originally published online on October 20, 2007
Journal of the London Mathematical Society 2007 76(2):498-512; doi:10.1112/jlms/jdm072
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© 2007 London Mathematical Society

C (K)-representations and R-boundedness

B. de Pagter

Delft Institute of Applied Mathematics
Faculty EEMCS
Delft University of Technology
P.O. Box 5031, 2600 GA Delft
The Netherlands

W. J. Ricker

Math. -Geogr.Fakultät
Katholische Universität Eichstätt-Ingolstadt
D-85072 Eichstätt
Germany
werner.ricker@ku-eichstaett.de

R-bounded representations {Phi}:C(K) -> L(X), with K a compact Hausdorff space and X a Banach space, are characterized via integration against R-bounded spectral measures in X. The techniques are based on a careful analysis of certain cyclic spaces associated with {Phi}.

2000 Mathematics Subject Classification 46G10, 47A67 (primary); 47B40 (secondary).

Received April 5, 2006; revised January 4, 2007; published online October 20, 2007.


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