A COMPLETE CLASSIFICATION OF THE SPACES OF COMPACT OPERATORS ON C([1, alpha], l(p)) SPACES, 1 < p < 8

摘要

We complete the classification, upto isomorphism, of the spaces of compact operators on C([ 1, gamma], lp) spaces, 1 < p < infinity. In order to do this, we classify, upto isomorphism, the spaces of compact operators K(E, F), where E = C([1, lambda], l(p)) and F = C([1, xi], l(q)) for arbitrary ordinals lambda and xi and 1 < p <= q < infinity.