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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Weak amenability of module extensions of Banach algebras


Author: Yong Zhang
Journal: Trans. Amer. Math. Soc. 354 (2002), 4131-4151
MSC (2000): Primary 46H20; Secondary 47B47, 46H10, 46H25, 46H35
Published electronically: June 4, 2002
MathSciNet review: 1926868
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Abstract: We start by discussing general necessary and sufficient conditions for a module extension Banach algebra to be $n$-weakly amenable, for $n = 0,1,2,\cdots$. Then we investigate various special cases. All these case studies finally provide us with a way to construct an example of a weakly amenable Banach algebra which is not $3$-weakly amenable. This answers an open question raised by H. G. Dales, F. Ghahramani and N. Grønbæk.


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Additional Information

Yong Zhang
Affiliation: Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
Email: zhangy@cc.umanitoba.ca

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03039-8
PII: S 0002-9947(02)03039-8
Keywords: $n$-weakly amenable, module, dual module, derivation, operator algebra
Received by editor(s): August 23, 1999
Received by editor(s) in revised form: January 25, 2002
Published electronically: June 4, 2002
Additional Notes: Research supported by NSERC
Article copyright: © Copyright 2002 American Mathematical Society