Character pseudo-amenability of Banach algebras

Rasoul Nasr-Isfahani¹ ; Mehdi Nemati²

¹ Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156-83111, Iran
² School of Mathematics Institute for Research in Fundamental Sciences (IPM) Tehran, P.O. Box 19395-5746, Iran

Colloquium Mathematicum, Tome 132 (2013) no. 2, pp. 177-193.

Résumé

Let $\mathcal {A}$ be a Banach algebra and let $\phi $ be a nonzero character on $\mathcal {A}$. We introduce and study a new notion of amenability for $\mathcal {A}$ based on existence of a $\phi $-approximate diagonal by modifying the concepts of $\phi $-amenability and pseudo-amenability. We then apply these results to characterize $\phi $-pseudo-amenability of various Banach algebras related to locally compact groups such as group algebras, measure algebras, certain dual algebras and Lebesgue–Fourier algebras.

Détail

DOI : 10.4064/cm132-2-2

Keywords: mathcal banach algebra phi nonzero character mathcal introduce study notion amenability mathcal based existence phi approximate diagonal modifying concepts phi amenability pseudo amenability apply these results characterize phi pseudo amenability various banach algebras related locally compact groups group algebras measure algebras certain dual algebras lebesgue fourier algebras