The Kreĭ n-Milman property and complemented bushes in Banach spaces

Aggie Ho

Vol. 98 (1982), No. 2, 347–363

DOI: 10.2140/pjm.1982.98.347

Abstract

We give “complementation” as a sufficient condition on a bush in a Banach space for the space to fail the Krein-Milman property. We also construct an example of a Banach space X which contains a complemented bush. Hence the space X fails the Krein-Milman property. However the closed convex span of the bush contains infinitely many extreme points and no denting points. Moreover, the closed convex span of these extreme points contains the original bush.

Mathematical Subject Classification 2000

Primary: 46B20

Milestones

Received: 3 September 1980

Revised: 12 December 1980

Published: 1 February 1982