International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 16, Pages 2533-2545
doi:10.1155/IJMMS.2005.2533
Double-dual types over the Banach space C(K)
Department of Mathematics, Indiana University East, Richmond 47374, IN, USA
Received 27 February 2005; Revised 5 July 2005
Copyright © 2005 Markus Pomper. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let K be a compact Hausdorff space and C(K) the Banach space
of all real-valued continuous functions on K, with the sup-norm.
Types over C(K) (in the sense of Krivine and Maurey) can be
uniquely represented by pairs (ℓ,u) of bounded real-valued
functions on K, where ℓ is lower semicontinuous, u is upper semicontinuous, ℓ≤u, and ℓ(x)=u(x) for all
isolated points x of K. A condition that characterizes the pairs (ℓ,u) that represent double-dual types over C(K) is given.