Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
• # Artykuł - szczegóły

## Studia Mathematica

2007 | 182 | 3 | 205-213

## Weak amenability of the second dual of a Banach algebra

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.

205-213

wydano
2007

### Twórcy

autor
• Department of Mathematics, University of Semnan, Semnan, Iran
autor
• Department of Mathematical Sciences, University of Oulu, Oulu 90014, Finland