Essential character amenability of Banach algebras

ESSENTIAL CHARACTER AMENABILITY OF BANACH ALGEBRAS

RASOUL NASR-ISFAHANI

 MEHDI NEMATI

Abstract:
For a Banach algebra A and a character  on A, we introduce and study the notion of essential amenability
of A. We give some examples to show that the class of essentially -amenable Banach
algebras is larger than that of -amenable Banach algebras introduced by Kaniuth et al. [‘On amenability
of Banach algebras’, Math. Proc. Cambridge Philos. Soc. 144 (2008), 85–96]. Finally,
we characterize the essential -amenability of various Banach algebras related to locally compact groups.
2010 Mathematics subject classification: primary 43A07, 46H05; secondary 43A20.
Keywords and phrases: Banach algebra, character amenability, essential amenability, locally compact
group.