On character amenable Banach algebras

• Autorzy: Z. Hu , M. Sangani Monfared , T. Traynor
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 43A30: Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc.
• 46H25: Normed modules and Banach modules, topological modules (if not placed in \SbjNo 13-XX or \SbjNo 16-XX)
• 46H20: Structure, classification of topological algebras
• 43A40: Character groups and dual objects
• 22D15: Group algebras of locally compact groups
• 43A20: L 1 -algebras on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 193
• Numer: 1
• Strony: 53-78

Daty

wydano

2009

Twórcy

autor

Z. Hu

• Department of Mathematics and Statistics, University of Windsor, Windsor, ON, Canada N9B 3P4

autor

M. Sangani Monfared

• Department of Mathematics and Statistics, University of Windsor, Windsor, ON, Canada N9B 3P4

autor

T. Traynor

• Department of Mathematics and Statistics, University of Windsor, Windsor, ON, Canada N9B 3P4

Identyfikatory

DOI

10.4064/sm193-1-3