On ϕ-amenability of Banach algebras

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

doi:10.1017/s0305004107000874

Cited by 122 publications

(125 citation statements)

References 14 publications

Supporting

Mentioning

125

Contrasting

Order By: Relevance

“…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%

See 1 more Smart Citation

On character amenable Banach algebras

Monfared

Traynor

2009

Studia Math.

View full text Add to dashboard Cite

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.

show abstract

“…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.

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

show abstract

“…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%