Turkish Journal of Mathematics

Abstract: Variety of Banach algebras is a non-empty class of Banach algebras in which there exist a family of laws such that all of its members satisfy all of the laws. In this paper, we have used merely mathematical items such as Banach algebras and varieties including Banach algebras in order to change the space of all varieties of Banach algebras into a compact metric space. We prove some theorems in the metric space of zero at infinity varieties, define the ^*-varieties of ^*-algebra and prove many theorems about ^*-varieties of C^*-algebras.

Key Words: Variety of Banach algebras, H-variety, Q-algebras, IR-algebras