Algebraically defined varieties of Banach algebras

Abstract

There exists a large extent of literature on the varieties of algebraic objects suth as groups and associative algebras. Earlier much attention has been focused around the varieties of topologico-algebraic objects such as topological groups, topological vector spaces and topological algebras. In this paper we consider the varieties of Banach algebras defined by polynomial identities and we show that There exists a one-to-one correspondence between the class of this varieties and closed T-ideals of the countably generated free algebra �� . Also we derive a result about the maximal ideals of �� .