Projections onto the subspace of compact operators

Abstract

THEOREM. Suppose U and V are Banach spaces and that there are bounded projections Px from U onto X and P2 from V onto Y. Then there are no bounded projections from the space of bounded operators on U into V onto the closed subspace of compact operators, in the following cases: 1. X is isomorphic [1] to /, 1 , c0 or c. 3. X is isomorphic to c; Y is isomorphic to /°°.