On ϕ-amenability of Banach algebras

Kaniuth, Eberhard; Lau, Anthony To-Ming; Pym, J. S.

doi:10.1017/s0305004107000874

Cited by 119 publications

(125 citation statements)

References 14 publications

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“…Identifying E with its natural image in E * * , we define g = D * * (Ψ )| E . Then a proof similar to that of [23,Theorem 1.1] shows that D = δ g if ψ = 0, and…”

Section: Recall That a Banach Algebramentioning

confidence: 82%

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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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“…Identifying E with its natural image in E * * , we define g = D * * (Ψ )| E . Then a proof similar to that of [23,Theorem 1.1] shows that D = δ g if ψ = 0, and…”

Section: Recall That a Banach Algebramentioning

confidence: 82%

“…If a Banach algebra is both left and right character amenable, it is called character amenable. The concept of (right) φ-amenable Banach algebras was introduced recently by Kaniuth, Lau, and Pym in [23] (see also [24]). Character amenability was introduced independently by the second named author in [36].…”

mentioning

confidence: 99%

On character amenable Banach algebras

Monfared

Traynor

2009

Studia Math.

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“…Let A be a Banach algebra and σ(A) be the carrier space of A, and let ϕ ∈ σ(A) be a homomorphism from A onto C. The notion of character amenability of Banach algebras was defined by Monfared in [18]. Meanwhile, the concept of ϕ-amenability of Banach algebras was introduced by Kaniuth and et al in [13]. These concepts were related to those cited in the work of Professor Lau in [16].…”

Section: Introductionmentioning

confidence: 99%

“…Also, according to [13], the Banach algebra A is ϕ-amenable (ϕ ∈ σ(A)) if there exists a bounded linear functional m on A * satisfying m(ϕ) = 1 and m(f · a) = ϕ(a)m(f ) for all a ∈ A and f ∈ A * . Therefore, the Banach algebra A is CA if and only if A is ϕ-amenable, for every ϕ ∈ σ(A) ∪ {0}.…”

Section: Introductionmentioning

confidence: 99%

Some Characterizations of Character Amenable Banach Algebras

Gordji¹,

Jabbari²,

Kim³

2015

Bulletin of the Korean Mathematical Society

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“…The concept of left amenability for a Lau algebra (a predual of a von Neumann algebra for which the identity of the dual is a multiplicative linear functional, [6]) has been extensively extended for an arbitrary Banach algebra by introducing the notion of ϕ−amenability in Kaniuth et al [4]. A Banach algebra A was called ϕ-amenable (ϕ ∈ △(A) = the spectrum of A) if there exists a m ∈ A * * satisfying m(ϕ) = 1 and m(f · a) = ϕ(a)m(f ) (a ∈ A, f ∈ A * ).…”

Section: Introductionmentioning

confidence: 99%