On spaces of operators on $C(Q)$ spaces ($Q$ countable metric space)

Abstract

In this paper we study spaces of nuclear operators Af(C(Q)) and spaces of compact operators K(C(Q)) on spaces of continuous functions C(Q), where Q is a countable compact metric space, in connection with the C. Bessaga and A. Pelczynski isomorphic classification of these spaces. We show that the spaces K(C(Q)) [resp. N(C(Q))] and K(C(Q')) [resp. N(C(Q'))] are isomorphic if, and only if, C(Q) and C(Q') are isomorphic. We show also that N(C(Q)) is not isomorphic to a subspace of K(C(Q)).