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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Amenability and weak amenability
of second conjugate Banach algebras


Authors: F. Ghahramani, R. J. Loy and G. A. Willis
Journal: Proc. Amer. Math. Soc. 124 (1996), 1489-1497
MSC (1991): Primary 46H20; Secondary 43A20
MathSciNet review: 1307520
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Abstract: For a Banach algebra $\mathfrak {A}$, amenability of $\mathfrak {A}^{**}$ necessitates amenability of $\mathfrak {A}$, and similarly for weak amenability provided $\mathfrak {A}$ is a left ideal in $\mathfrak {A}^{**}$. For $\mathfrak {G}$ a locally compact group, indeed more generally, $L^1(\mathfrak {G})^{**}$ is amenable if and only if $\mathfrak {G}$ is finite. If $L^1(\mathfrak {G})^{**}$ is weakly amenable, then $M(\mathfrak {G})$ is weakly amenable.


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Additional Information

F. Ghahramani
Affiliation: Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2
Email: ghahram@cc.umanitoba.ca

R. J. Loy
Affiliation: Department of Mathematics, Australian National University, ACT 0200, Australia
Email: loyrmath@durras.anu.edu.au

G. A. Willis
Affiliation: Department of Mathematics, The University of Newcastle, Newcastle 2308, Australia
Email: george@frey.newcastle.edu.au

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03177-2
PII: S 0002-9939(96)03177-2
Keywords: Amenability, locally compact group, second conjugate space
Received by editor(s): June 27, 1994
Received by editor(s) in revised form: October 19, 1994
Communicated by: Theodore Gamelin
Article copyright: © Copyright 1996 American Mathematical Society