Character pseudo-amenability of Banach algebras
Volume 132 / 2013
Colloquium Mathematicum 132 (2013), 177-193
MSC: 43A07, 46H05, 46H25.
DOI: 10.4064/cm132-2-2
Abstract
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.
