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Bounded and completely bounded local derivations from certain commutative semisimple Banach algebras
Author(s):
Ebrahim
Samei
Journal:
Proc. Amer. Math. Soc.
133
(2005),
229-238.
MSC (2000):
Primary 46L07, 47B47
Posted:
July 26, 2004
MathSciNet review:
2085174
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Abstract:
We show that for a locally compact group  , every completely bounded local derivation from the Fourier algebra  into a symmetric operator  -module or the operator dual of an essential  -bimodule is a derivation. Moreover, for amenable  we show that the result is true for all operator  -bimodules. In particular, we derive a new proof to a result of N. Spronk that  is always operator weakly amenable.
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Additional Information:
Ebrahim
Samei
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2
Email:
umsameie@cc.umanitoba.ca
DOI:
10.1090/S0002-9939-04-07555-0
PII:
S 0002-9939(04)07555-0
Keywords:
Local derivations,
Fourier algebra,
operator space,
operator weak amenability
Received by editor(s):
June 13, 2003
Received by editor(s) in revised form:
September 30, 2003
Posted:
July 26, 2004
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2004,
American Mathematical Society
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