Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Approximate amenability of Schatten classes, Lipschitz algebras and second duals of Fourier algebras
AU - Choi, Yemon
AU - Ghahramani, Fereidoun
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
U2 - 10.1093/qmath/hap034
DO - 10.1093/qmath/hap034
M3 - Journal article
VL - 62
SP - 39
EP - 58
JO - The Quarterly Journal of Mathematics
JF - The Quarterly Journal of Mathematics
SN - 0033-5606
IS - 1
ER -