Weak amenability of the second dual of a Banach algebra

M. Eshaghi Gordji, and M. Filali. "Weak amenability of the second dual of a Banach algebra." Studia Mathematica 182.3 (2007): 205-213. <http://eudml.org/doc/284386>.

@article{M2007,
abstract = {It is known that a Banach algebra inherits amenability from its second Banach dual **. 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 which are left ideals in **, the dual Banach algebras, and the Banach algebras which are Arens regular and have every derivation from into * weakly compact. In this paper, we extend this class of algebras to the Banach algebras for which the second adjoint of each derivation D: → * satisfies D”(**)⊆ WAP(), the Banach algebras which are right ideals in ** and satisfy ** = **, 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.},
author = {M. Eshaghi Gordji, M. Filali},
journal = {Studia Mathematica},
keywords = {derivation; weak amenability; Arens product},
language = {eng},
number = {3},
pages = {205-213},
title = {Weak amenability of the second dual of a Banach algebra},
url = {http://eudml.org/doc/284386},
volume = {182},
year = {2007},
}

TY - JOUR
AU - M. Eshaghi Gordji
AU - M. Filali
TI - Weak amenability of the second dual of a Banach algebra
JO - Studia Mathematica
PY - 2007
VL - 182
IS - 3
SP - 205
EP - 213
AB - It is known that a Banach algebra inherits amenability from its second Banach dual **. 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 which are left ideals in **, the dual Banach algebras, and the Banach algebras which are Arens regular and have every derivation from into * weakly compact. In this paper, we extend this class of algebras to the Banach algebras for which the second adjoint of each derivation D: → * satisfies D”(**)⊆ WAP(), the Banach algebras which are right ideals in ** and satisfy ** = **, 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.
LA - eng
KW - derivation; weak amenability; Arens product
UR - http://eudml.org/doc/284386
ER -