SOME RESULTS OF THE KA-APPROXIMATION PROPERTY FOR BANACH SPACES

Given a Banach operator ideal A, we investigate the approximation property related to the ideal of A-compact operators, K-A-AP. We prove that a Banach space X has the K-A-AP if and only if there exists lambda >= 1 such that for every Banach space Y and every R is an element of K-A(Y, X), R is an element of <({SR : S is an element of F(X, X), vertical bar vertical bar SR vertical bar vertical bar K-A <= lambda vertical bar vertical bar R vertical bar vertical bar K-A})over bar>(tau c). For a surjective, maximal and right-accessible Banach operator ideal A, we prove that a Banach space X has the K-(Aadj)dual-AP if the dual space of X has the K-A-AP.