Weak amenability of triangular Banach algebras

Authors:
B. E. Forrest and L. W. Marcoux

Journal:
Trans. Amer. Math. Soc. **354** (2002), 1435-1452

MSC (2000):
Primary 46H25, 16E40

DOI:
https://doi.org/10.1090/S0002-9947-01-02957-9

Published electronically:
December 4, 2001

MathSciNet review:
1873013

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Abstract: Let and be unital Banach algebras, and let be a Banach -module. Then becomes a *triangular Banach algebra* when equipped with the Banach space norm . A Banach algebra is said to be *-weakly amenable* if all derivations from into its dual space are inner. In this paper we investigate Arens regularity and -weak amenability of a triangular Banach algebra in relation to that of the algebras , and their action on the module .

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Additional Information

**B. E. Forrest**

Affiliation:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Email:
beforres@math.uwaterloo.ca

**L. W. Marcoux**

Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

Address at time of publication:
Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1

Email:
L.Marcoux@ualberta.ca, LWMarcoux@math.uwaterloo.ca

DOI:
https://doi.org/10.1090/S0002-9947-01-02957-9

Received by editor(s):
October 9, 1998

Received by editor(s) in revised form:
July 20, 1999

Published electronically:
December 4, 2001

Additional Notes:
Research supported in part by NSERC (Canada)

Article copyright:
© Copyright 2001
American Mathematical Society