On function and operator modules

Authors:
David Blecher and Christian Le Merdy

Journal:
Proc. Amer. Math. Soc. **129** (2001), 833-844

MSC (2000):
Primary 47L30, 47L25; Secondary 46H25, 46J10, 46L07

DOI:
https://doi.org/10.1090/S0002-9939-00-05866-4

Published electronically:
August 30, 2000

MathSciNet review:
1802002

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Abstract: Let be a unital Banach algebra. We give a characterization of the left Banach -modules for which there exists a commutative unital -algebra , a linear isometry , and a contractive unital homomorphism such that for any . We then deduce a ``commutative" version of the Christensen-Effros-Sinclair characterization of operator bimodules. In the last section of the paper, we prove a -version of the latter characterization, which generalizes some previous work of Effros and Ruan.

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Additional Information

**David Blecher**

Affiliation:
Department of Mathematics, University of Houston, Houston, Texas 77204-3476

Email:
dblecher@math.uh.edu

**Christian Le Merdy**

Affiliation:
Département de Mathématiques, Université de Franche-Comté, 25030 Besançon Cedex, France

DOI:
https://doi.org/10.1090/S0002-9939-00-05866-4

Received by editor(s):
May 24, 1999

Published electronically:
August 30, 2000

Communicated by:
David R. Larson

Article copyright:
© Copyright 2000
American Mathematical Society