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 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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm182-3-2,
author = {M. Eshaghi Gordji and M. Filali},
title = {Weak amenability of the second dual of a Banach algebra},
journal = {Studia Mathematica},
volume = {178},
year = {2007},
pages = {205-213},
zbl = {1135.46027},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm182-3-2}
}
M. Eshaghi Gordji; M. Filali. Weak amenability of the second dual of a Banach algebra. Studia Mathematica, Tome 178 (2007) pp. 205-213. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm182-3-2/