Approximate Identities in Algebras of Compact Operators on Frechet Spaces

Abstract

Bounded approximate identity(bai) is a key concept in the theory of amenability of algebras. In this paper, we show that algebra of compact operators  on Frechet space X has both the right and left locally bounded approximate identities. Sufficient conditions for the existence of these identities are  established based on the geometry properties of the Frechet space X and its dual space X0 respectively.