Isomorphisms of spaces of norm-continuous functions

Michael James Cambern

Vol. 116 (1985), No. 2, 243–254

DOI: 10.2140/pjm.1985.116.243

Abstract

If X and Y are compact Hausdorff spaces and E a uniformly convex Banach space, then the existence of an isomorphism T of C(X,E) onto C(Y,E) with ∥T∥∥T⁻¹∥ small implies that X and Y are homeomorphic.

Mathematical Subject Classification 2000

Primary: 46E40

Milestones

Received: 9 September 1983

Published: 1 February 1985