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 X' respectively.

On Certain Spaces of Ideal Operators

“…Its notions therefore generalize Banach space and Hilbert spaces. Any algebra A equipped with a structure of lcs with respect to which the product is separately continuous is a topological algebra [3]. So, a Frechet algebra is a complete topological algebra of which an increasing countable collection {pi; i ∈ N} of sub-multiplicative continuous semi-norms determines its topology.…”