Amenability and weak amenability of second conjugate Banach algebras
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- by F. Ghahramani, R. J. Loy and G. A. Willis PDF
- Proc. Amer. Math. Soc. 124 (1996), 1489-1497 Request permission
Addendum: Proc. Amer. Math. Soc. 148 (2020), 4573-4575.
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.References
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Additional Information
- F. Ghahramani
- Affiliation: Department of Mathematics and Astronomy, University of Manitoba, Winnipeg, Canada R3T 2N2
- MR Author ID: 196713
- Email: ghahram@cc.umanitoba.ca
- R. J. Loy
- Affiliation: Department of Mathematics, Australian National University, ACT 0200, Australia
- MR Author ID: 116345
- Email: loyrmath@durras.anu.edu.au
- G. A. Willis
- Affiliation: Department of Mathematics, The University of Newcastle, Newcastle 2308, Australia
- MR Author ID: 183250
- Email: george@frey.newcastle.edu.au
- Received by editor(s): June 27, 1994
- Received by editor(s) in revised form: October 19, 1994
- Communicated by: Theodore Gamelin
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 1489-1497
- MSC (1991): Primary 46H20; Secondary 43A20
- DOI: https://doi.org/10.1090/S0002-9939-96-03177-2
- MathSciNet review: 1307520