A note on generalized approximation property

We introduce a notion of generalized approximation property,which we refer to as l s-ap possessed by a banach space x,corresponding to an arbitrary banach sequence space and a convex subset l s (x) of (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 l s - -ap with the help of -compact operators,-nuclear operators,and quasi- -nuclear operators. a particular case for = l p (1 ≤ p ≤ ∞) has also been characterized. © 2013 antara bhar and manjul gupta.