International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 16, Pages 2533-2545
Double-dual types over the Banach space
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.
Let be a compact Hausdorff space and the Banach space
of all real-valued continuous functions on , with the sup-norm.
Types over (in the sense of Krivine and Maurey) can be
uniquely represented by pairs of bounded real-valued
functions on , where is lower semicontinuous, is upper semicontinuous, , and for all
isolated points of . A condition that characterizes the pairs that represent double-dual types over is given.