A remark on the containment of <i>c</i>₀ in spaces of compact operators

Abstract

Let X, Y be two Banach spaces. By L(X, Y) (resp. K(X, Y) ) we denote the Banach space of all bounded, linear (resp. compact, bounded, linear) operators from X into Y . Several papers have been devoted to the question of when c 0 embeds isomorphically into K(X, Y) (see 5, 8, 9 and their references) and its relationship with the following question: (i) is K(X, Y) always uncomplemented in L(X, Y) when L(X, Y) K(X, Y) ?