On character amenable Banach algebras

Z. Hu, M. Sangani Monfared, and T. Traynor. "On character amenable Banach algebras." Studia Mathematica 193.1 (2009): 53-78. <http://eudml.org/doc/284445>.

@article{Z2009,
abstract = {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.},
author = {Z. Hu, M. Sangani Monfared, T. Traynor},
journal = {Studia Mathematica},
keywords = {Banach algebras; character amenability; character amenability constant; locally compact groups; uniform algebras},
language = {eng},
number = {1},
pages = {53-78},
title = {On character amenable Banach algebras},
url = {http://eudml.org/doc/284445},
volume = {193},
year = {2009},
}

TY - JOUR
AU - Z. Hu
AU - M. Sangani Monfared
AU - T. Traynor
TI - On character amenable Banach algebras
JO - Studia Mathematica
PY - 2009
VL - 193
IS - 1
SP - 53
EP - 78
AB - 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.
LA - eng
KW - Banach algebras; character amenability; character amenability constant; locally compact groups; uniform algebras
UR - http://eudml.org/doc/284445
ER -