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Approximate amenability of Schatten classes, Lipschitz algebras and second duals of Fourier algebras

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Approximate amenability of Schatten classes, Lipschitz algebras and second duals of Fourier algebras. / Choi, Yemon; Ghahramani, Fereidoun.
In: The Quarterly Journal of Mathematics, Vol. 62, No. 1, 2011, p. 39-58.

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Choi Y, Ghahramani F. Approximate amenability of Schatten classes, Lipschitz algebras and second duals of Fourier algebras. The Quarterly Journal of Mathematics. 2011;62(1):39-58. doi: 10.1093/qmath/hap034

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Choi, Yemon ; Ghahramani, Fereidoun. / Approximate amenability of Schatten classes, Lipschitz algebras and second duals of Fourier algebras. In: The Quarterly Journal of Mathematics. 2011 ; Vol. 62, No. 1. pp. 39-58.

Bibtex

@article{6f4f4d3844004b48a75b7ccdcf7f3d33,
title = "Approximate amenability of Schatten classes, Lipschitz algebras and second duals of Fourier algebras",
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.",
author = "Yemon Choi and Fereidoun Ghahramani",
year = "2011",
doi = "10.1093/qmath/hap034",
language = "English",
volume = "62",
pages = "39--58",
journal = "The Quarterly Journal of Mathematics",
issn = "0033-5606",
publisher = "Oxford University Press",
number = "1",

}

RIS

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 -