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The Quarterly Journal of Mathematics Advance Access published online on October 29, 2009
The Quarterly Journal of Mathematics, doi:10.1093/qmath/hap034
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© 2009. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

APPROXIMATE AMENABILITY OF SCHATTEN CLASSES, LIPSCHITZ ALGEBRAS AND SECOND DUALS OF FOURIER ALGEBRAS

Y. Choi{dagger}

Département de Mathématiques et de Statistique, Pavillon Alexandre-Vachon, Université Laval, Québec, QC, Canada G1V 0A6

F. Ghahramani {ddagger}

Department of Mathematics, Machray Hall, University of Manitoba, Winnipeg, MB, Canada R3T 2N2

{dagger} Corresponding author. E-mail: y.choi.97{at}cantab.net

Received 22 June 2009; revised 1 October 2009
  Abstract

Amenability of any of the algebras described in the title is known to force them to be finite-dimensional. The analogous problems for approximate amenability have been open for some years now. In this article we give a complete solution for the first two classes, using a new criterion for showing that certain Banach algebras without bounded approximate identities cannot be approximately amenable. The method also provides a unified approach to existing non-approximate amenability results, and is applied to the study of certain commutative Segal algebras. Using different techniques, we prove that bounded approximate amenability of the second dual of a Fourier algebra implies that it is finite-dimensional. Some other results for related algebras are obtained.

{ddagger} E-mail: fereidou{at}cc.umanitoba.ca


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