Proceedings of the American Mathematical Society

Author(s): F. Ghahramani; R. J. Loy; G. A. Willis
Journal: Proc. Amer. Math. Soc. 124 (1996), 1489-1497.
MSC (1991): Primary 46H20; Secondary 43A20
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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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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

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