Weak amenability of the second dual of a Banach algebra

• Autorzy: M. Eshaghi Gordji , M. Filali
• Języki publikacji: EN

Abstrakty

EN

It is known that a Banach algebra 𝒜 inherits amenability from its second Banach dual 𝒜**. No example is yet known whether this fails if one considers the weak amenability instead, but the property is known to hold for the group algebra L¹(G), the Fourier algebra A(G) when G is amenable, the Banach algebras 𝒜 which are left ideals in 𝒜**, the dual Banach algebras, and the Banach algebras 𝒜 which are Arens regular and have every derivation from 𝒜 into 𝒜* weakly compact. In this paper, we extend this class of algebras to the Banach algebras for which the second adjoint of each derivation D:𝒜 → 𝒜* satisfies D''(𝒜**)⊆ WAP(𝒜), the Banach algebras 𝒜 which are right ideals in 𝒜** and satisfy 𝒜**𝒜 = 𝒜**, and to the Figà-Talamanca-Herz algebra $A_p(G)$ for G amenable. We also provide a short proof of the interesting recent criterion on when the second adjoint of a derivation is again a derivation.

Kategorie tematyczne

• 46H20: Structure, classification of topological algebras
• 43A20: L 1 -algebras on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 182
• Numer: 3
• Strony: 205-213

Daty

wydano

2007

Twórcy

autor

M. Eshaghi Gordji

• Department of Mathematics, University of Semnan, Semnan, Iran

autor

M. Filali

• Department of Mathematical Sciences, University of Oulu, Oulu 90014, Finland

Identyfikatory

DOI

10.4064/sm182-3-2