THE IDEAL OF WEAKLY p-COMPACTOPERATORS AND ITS APPROXIMATIONPROPERTY FOR BANACH SPACES

摘要

We investigate the ideal Wp of weakly p-compact operatorsand its approximation property (Wp-AP).We prove that and that for 1 < p ≤ ∞, a Banach space X has the W p -AP if and only if the identity map on Xis approximated by finite rank operators on X in the topology of uniform convergence on weaklyp-compact sets. Also, we study the W p -AP for classical sequence spaces and dual spaces.