Banach algebras on semigroups and on their compactifications

Dales, H. G.; Lau, Anthony To-Ming; Strauss, Dona

doi:10.1090/s0065-9266-10-00595-8

Cited by 121 publications

(167 citation statements)

References 145 publications

(186 reference statements)

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“…Then L 1 (G) * * does not have any nonzero continuous point derivation corresponding to any character φ ∈ σ(L 1 (G) * * ). It follows from [4,Theorem 11.17] that G is finite.…”

Section: Examples Of Left Introverted Subspaces Of L ∞ (G) Containingmentioning

confidence: 99%

On character amenable Banach algebras

Monfared

Traynor

2009

Studia Math.

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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 ∼ = C n 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 L 1 (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.

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“…Then L 1 (G) * * does not have any nonzero continuous point derivation corresponding to any character φ ∈ σ(L 1 (G) * * ). It follows from [4,Theorem 11.17] that G is finite.…”

Section: Examples Of Left Introverted Subspaces Of L ∞ (G) Containingmentioning

confidence: 99%

On character amenable Banach algebras

Monfared

Traynor

2009

Studia Math.

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“…This Banach algebra has been considered by Dales and Duncan in [4]. Banach algebras similar to 1 (B) are considered in [5].…”

Section: Introductionmentioning

confidence: 99%

The Cyclic and Simplicial Cohomology of the Bicyclic Semigroup Algebra

Gourdeau

White

2010

The Quarterly Journal of Mathematics

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Abstract. Let A = 1 (B) be the semigroup algebra of B, the bicyclic semigroup. We give a resolution of ∞ (B) which simplifies the computation of the cohomology of 1 (B) dual bimodules. We apply this to the dual module ∞ (B) and show that the simplicial cohomology groups H n (A, A ) vanish for n ≥ 2. Using the Connes-Tzygan exact sequence, these results are used to show that the cyclic cohomology groups HC n (A, A ) vanish when n is odd and are one-dimensional when n is even (n ≥ 2).

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“…With this perspective it is also important that results about algebras 1 (S) are obtained with a minimal appeal to specific semi-group properties. In a recent treatise ( [4]), a rather encompassing account of Banach algebraic properties of semi-group algebras is given, in particular, the authors conclude the description of amenability in terms of algebraic properties of the semi-group ( [4,Theorem 10.12]). …”

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confidence: 99%