A Note on Generalized Approximation Property

Abstract EN

We introduce a notion of generalized approximation property, which we refer to as Ls-λ-AP possessed by a Banach space X, corresponding to an arbitrary Banach sequence space λ and a convex subset Ls(X) of ℒ(X), the class of bounded linear operators on X.

This property includes approximation property studied by Grothendieck, p-approximation property considered by Sinha and Karn and Delgado et al., and also approximation property studied by Lissitsin et al.

We characterize a Banach space having Ls-λ-AP with the help of λ-compact operators, λ-nuclear operators, and quasi-λ-nuclear operators.

A particular case for λ=lp (1≤p≤∞) has also been characterized.