TOPOLOGICAL DIRECT SUM DECOMPOSITIONS OF BANACH-SPACES

Let Y and Z be two closed subspaces of a Banach space X such that Y≠lcub;0rcub; and Y+Z=X. Then, if Z is weakly countably determined, there exists a continuous projection T in X such that ∥T∥=1, T(X)⊃Y, T -1(0)⊂Z and dens T(X)=dens Y. It follows that every Banach space X is the topological direct sum of two subspaces X 1 and X 2 such that X 1 is reflexive and dens X 2**=dens X**/X. © 1990 Hebrew University.