Module Amenability for Semigroup Algebras
By M. Amini. 2002
106 citations recorded by the source corpus.
AbstractWe extend the concept of amenability of a Banach algebra A to the case that there is an extra \A-module structure on A, and show that when S is an inverse semigroup with subsemigroup E of idempotents, then A = \ell1(S) as a Banach module over \A = \ell1(E) is module amenable if and only if S is amenable. When S is a discrete group, \ell1(E) = ℂ and this is just the Johnson’s theorem.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/27fc86103f43d7544a289826f44c751cd278efb1
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Module Arens regularity for semigroup algebras (2008, background): “The second author in [1] introduced the concept of module amenability and showed that for an inverse semigroup S, the semigroup algebra 1(S) is module amenable as a Banach module on 1(E), where E is the set of idempotents of S, if and only if S is amenable.”
- Module amenability of the second dual and module topological center of semigroup algebras (2009, background): “The first author in [1] introduced the concept of module amenability and showed that for an inverse semigroup S, the semigroup algebra l(1)(S) is module amenable as a Banach module on l(1)(E), where E is the set of idempotents of S, if and only if S is amenable (see also [2]).”