Let 𝓐 be a Banach algebra and let ϕ be a nonzero character on 𝓐. We introduce and study a new notion of amenability for 𝓐 based on existence of a ϕ-approximate diagonal by modifying the concepts of ϕ-amenability and pseudo-amenability. We then apply these results to characterize ϕ-pseudo-amenability of various Banach algebras related to locally compact groups such as group algebras, measure algebras, certain dual algebras and Lebesgue-Fourier algebras.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-2-2,
author = {Rasoul Nasr-Isfahani and Mehdi Nemati},
title = {Character pseudo-amenability of Banach algebras},
journal = {Colloquium Mathematicae},
volume = {131},
year = {2013},
pages = {177-193},
zbl = {1290.43006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-2-2}
}
Rasoul Nasr-Isfahani; Mehdi Nemati. Character pseudo-amenability of Banach algebras. Colloquium Mathematicae, Tome 131 (2013) pp. 177-193. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm132-2-2/