Generalized notions of amenability, II

F. Ghahramani; R. J. Loy; Y. Zhang

doi:10.1016/j.jfa.2007.12.011

Generalized notions of amenability, II

F. Ghahramani^*, R. J. Loy, Y. Zhang

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

83 Citations (Scopus)

Abstract

This paper continues the investigation of the first two authors begun in part I. It is shown that approximate amenability and approximate contractibility are the same properties, as are uniform approximate amenability and amenability. Bounded approximate contractibility and bounded approximate amenability are characterized by the existence of suitable operator bounded approximate identities for the diagonal ideal. Results are given on Banach sequence algebras, Lipschitz algebras and Beurling algebras, and on the crucial role of approximate identities. A new proof is given for a result due to N. Grønbæk on characterizing of amenability for Beurling algebras.

Original language	English
Pages (from-to)	1776-1810
Number of pages	35
Journal	Journal of Functional Analysis
Volume	254
Issue number	7
DOIs	https://doi.org/10.1016/j.jfa.2007.12.011
Publication status	Published - 1 Apr 2008

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abstract = "This paper continues the investigation of the first two authors begun in part I. It is shown that approximate amenability and approximate contractibility are the same properties, as are uniform approximate amenability and amenability. Bounded approximate contractibility and bounded approximate amenability are characterized by the existence of suitable operator bounded approximate identities for the diagonal ideal. Results are given on Banach sequence algebras, Lipschitz algebras and Beurling algebras, and on the crucial role of approximate identities. A new proof is given for a result due to N. Gr{\o}nb{\ae}k on characterizing of amenability for Beurling algebras.",

keywords = "Amenable Banach algebra, Amenable group, Approximate diagonal, Approximate identity, Approximately amenable Banach algebra, Beurling algebras, Derivation",

author = "F. Ghahramani and Loy, {R. J.} and Y. Zhang",

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AU - Ghahramani, F.

AU - Loy, R. J.

AU - Zhang, Y.

PY - 2008/4/1

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N2 - This paper continues the investigation of the first two authors begun in part I. It is shown that approximate amenability and approximate contractibility are the same properties, as are uniform approximate amenability and amenability. Bounded approximate contractibility and bounded approximate amenability are characterized by the existence of suitable operator bounded approximate identities for the diagonal ideal. Results are given on Banach sequence algebras, Lipschitz algebras and Beurling algebras, and on the crucial role of approximate identities. A new proof is given for a result due to N. Grønbæk on characterizing of amenability for Beurling algebras.

AB - This paper continues the investigation of the first two authors begun in part I. It is shown that approximate amenability and approximate contractibility are the same properties, as are uniform approximate amenability and amenability. Bounded approximate contractibility and bounded approximate amenability are characterized by the existence of suitable operator bounded approximate identities for the diagonal ideal. Results are given on Banach sequence algebras, Lipschitz algebras and Beurling algebras, and on the crucial role of approximate identities. A new proof is given for a result due to N. Grønbæk on characterizing of amenability for Beurling algebras.

KW - Amenable Banach algebra

KW - Amenable group

KW - Approximate diagonal

KW - Approximate identity

KW - Approximately amenable Banach algebra

KW - Beurling algebras

KW - Derivation

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DO - 10.1016/j.jfa.2007.12.011

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VL - 254

SP - 1776

EP - 1810

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 7

ER -

Generalized notions of amenability, II

Abstract

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