Hereditary properties of Amenability modulo an ideal of Banach algebras

Abstract

<p>In this paper we investigate some hereditary properties of amenability modulo an ideal of Banach algebras. We show that<br />if $(e_{\alpha})_{\alpha}$ is a bounded approximate identity modulo $I$ of a Banach algebra $A$ and $X$ is a neo-unital modulo $I$, then $(e_{\alpha})_{\alpha}$ is a bounded approximate identity for $X$. Moreover we show that amenability modulo an ideal of a Banach algebra $A$ can be only considered by the neo-unital modulo $I$ Banach algebra over $A$</p