Generalized notions of amenability, II
TLDR
In this article, it was shown that approximate amenability and approximate contractibility are the same properties, as are uniform approximate contractability and amenability, and the existence of suitable operator bounded approximate identities for the diagonal ideal.About:
This article is published in Journal of Functional Analysis.The article was published on 2004-03-01 and is currently open access. It has received 177 citations till now. The article focuses on the topics: Approximate identity & Bounded function.read more
Citations
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Banach Algebras on Semigroups and on Their Compactifications
TL;DR: In this article, the authors studied the structure of the second dual of the semigroup algebra and its amenability constant, showing that there are 'forbidden values' for this constant.
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Pseudo-amenable and pseudo-contractible Banach algebras
F. Ghahramani,Yong Zhang +1 more
TL;DR: In this paper, the authors introduce and study two new notions of amenability for Banach algebras, and compare these notions with some of those studied earlier, including the notions of locally compact groups.
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On character amenable Banach algebras
TL;DR: Character amenability is a cohomological property weaker than the classical amenability introduced by B.E. Johnson as discussed by the authors, and it is characterized in terms of bounded approximate identities and certain topologically invariant elements of the second dual.
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Approximate and pseudo-amenability of various classes of Banach algebras
TL;DR: In this article, it was shown that every boundedly approximately contractible Banach algebra has a bounded approximate identity, and that the Fourier algebra of the free group on two generators is not operator approximately amenable.
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Approximate amenability for Banach sequence algebras
TL;DR: In this paper, the authors consider when certain Banach sequence algebras A on the set N are approximately amenable and resolve the special cases where A =lp for 1 ≤ p < ∞.
References
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Abstract Harmonic Analysis
Edwin Hewitt,Kenneth A. Ross +1 more
TL;DR: The first € price and the £ and $ price are net prices, subject to local VAT as discussed by the authors, and prices and other details are subject to change without notice. All errors and omissions excepted.
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Banach algebras and automatic continuity
TL;DR: Banach algebras combine algebraic and analytical aspects: it is the interplay of these structures that gives the subject its fascination as discussed by the authors, and shows how their topology is often determined by their algebraic structure.