Representations of convex nondentable sets

Spiros Argyros and Irene Deliyanni

Vol. 155 (1992), No. 1, 29–70

DOI: 10.2140/pjm.1992.155.29

Abstract

It is proved that every closed convex non-R.N.P. set in a Banach space contains a non-dentable subset with a martingale coordinatization. Thus we answer affirmatively a question posed by H. Rosenthal and A. Wessel. The proof depends on the concept of the Convex Finite-Dimensional Schauder Decomposition (C.F.D.S.D.) introduced and investigated in the present paper. Certain partial positive results are also given related to the following fundamental problem: Every closed convex set either is R.N.P. or it contains a closed subset with a Pal-representation.

Mathematical Subject Classification 2000

Primary: 46B22

Milestones

Received: 10 September 1990

Revised: 2 July 1991

Published: 1 September 1992