Isomorphisms into section spaces of Banach bundles

Abstract

Let X be a compact Hausdorff space, E a (real) Banach space, and let C(X, E) be the space of continuous functions from X to E. The monograph of Cembranos and Mendoza provides a primer on when C (X, E) might contain isomorphic copies of the classical spaces c ₀, l ¹, and l ^∞. In this paper, we investigate what isomorphisms of classical spaces might occur if the continuous vector-valued functions on X take their values in spaces which may vary over X.