Spaces of operators and c(0)

Bessaga and Pelczynski showed that if c(0) embeds in the dual X* of a Banac h space X, then l(infinity) embeds complementably in X, and l(infinity) emb eds as a subspace of X*. In this note the Diestel-Faires theorem and techni ques of Kalton are used to show that if X is an infinite-dimensional Banach space, Y is an arbitrary Banach space, and c(0) embeds in L(X,Y), then l(i nfinity) embeds in L(X,Y), and l(1) embeds complementably in X circle times (gamma) Y*. Applications to embeddings of c(0) in various spaces of operat ors are given.