The Uncomplemented Subspace K(X,Y)

Abstract

AbstractA vector measure result is used to study the complementation of the space K(X,Y) of compact operators in the spaces W(X,Y) of weakly compact operators, CC(X,Y) of completely continuous operators, and U(X,Y) of unconditionally converging operators. Results of Kalton and Emmanuele concerning the complementation of K(X,Y) in L(X,Y) and in W(X,Y) are generalized. The containment of c0 and ℓ∞ in spaces of operators is also studied.