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Reflexive Representations and Banach C*-Modules

Published online by Cambridge University Press:  20 November 2018

Don Hadwin  and
Mehmet Orhon
Don Hadwin
Affiliation:
Mathematics Department, University of New Hampshire, Durham, NH 03824, e-mail: don@math.unh.edu
Mehmet Orhon
Affiliation:
RR2 Box 5465, Union, ME 04862
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Abstract

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Suppose A is a unital C*-algebra and m:A → B(X) is unital bounded algebra homomorphism where B(X) is the algebra of all operators on a Banach space X. When X is a Hilbert space, a problem of Kadison [9] asks whether m is similar to a *-homomorphism. Haagerup [5] has shown that the answer is positive when m(A) has a cyclic vector or whenever m is completely bounded. We use this to show m(A) is reflexive (Alg Lat m(A) = m(A)−sot) whenever X is a Hilbert space. Our main result is that whenever A is a separable GCR C*-algebra and X is a reflexive Banach space, then m(A) is reflexive.

Keywords

Primary: 47D30Secondary46L99
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 40 , Issue 4 , 01 December 1997 , pp. 443 - 447
Copyright
Copyright © Canadian Mathematical Society 1997

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