We obtain characterizations of left character amenable Banach algebras in terms of the existence of left ϕ-approximate diagonals and left ϕ-virtual diagonals. We introduce the left character amenability constant and find this constant for some Banach algebras. For all locally compact groups G, we show that the Fourier-Stieltjes algebra B(G) is C-character amenable with C < 2 if and only if G is compact. We prove that if A is a character amenable, reflexive, commutative Banach algebra, then A ≅ ℂⁿ for some n ∈ ℕ. We show that the left character amenability of the double dual of a Banach algebra A implies the left character amenability of A, but the converse statement is not true in general. In fact, we give characterizations of character amenability of L¹(G)** and A(G)**. We show that a natural uniform algebra on a compact space X is character amenable if and only if X is the Choquet boundary of the algebra. We also introduce and study character contractibility of Banach algebras.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-1-3,
author = {Z. Hu and M. Sangani Monfared and T. Traynor},
title = {On character amenable Banach algebras},
journal = {Studia Mathematica},
volume = {192},
year = {2009},
pages = {53-78},
zbl = {1175.22005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-1-3}
}
Z. Hu; M. Sangani Monfared; T. Traynor. On character amenable Banach algebras. Studia Mathematica, Tome 192 (2009) pp. 53-78. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm193-1-3/