Generalized notions of amenability, II

By F. Ghahramani, R. J. Loy, Yong Zhang. 2004

165 citations recorded by the source corpus.

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. Gronbaek on characterizing of amenability for Beurling algebras.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e38f60d9119829e4f53cd8ec448db09d7615be1d

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

Approximate amenability for Banach sequence algebras (2006, background): “independently by Pirkovskii [10] and Ghahramani [ 4 ] that a uniformly approximately amenable Banach algebra is already amenable.”
Banach Algebras on Semigroups and on Their Compactifications (2010, background): “The basic properties of approximately amenable Banach algebras were established in [51]; further results are given in [55].”
Biflatness and Pseudo-Amenability of Segal Algebras (2008, methodology): “e [21]. A natural relaxation of amenability is to allow Ato admit a diagonal net, as in (1) above, but not insist that it is bounded. In doing so we obtain (operator) pseudo-amenability, as deﬁned in [14]. If Aadmits a net in A⊗bA(resp. in A⊗bopA) which satisﬁes (1), and the additional property that”
On character amenable Banach algebras (2009, background): “Over the years, many different variations of amenability have been introduced, among which one can mention: weak amenability by Bade, Curtis and Dales [2], approximate amenability by Ghahramani and Loy [16] , operator amenability by Z.”