On Peł czyński’s properties (V) and (V^∗)

Elias Saab and Paulette Saab

Vol. 125 (1986), No. 1, 205–210

DOI: 10.2140/pjm.1986.125.205

Abstract

It is shown that a Banach lattice X has Pelczynski’s property (V ^∗) if and only if X contains no subspace isomorphic to c₀. This result is used to show that there is a Banach space E that has Pelczynski’s property (V ^∗) but such that its dual E^∗ fails Pelczynski’s property (V), thus answering in the negative a question of Pelczynski.

Mathematical Subject Classification 2000

Primary: 46B20

Secondary: 46B30

Milestones

Received: 14 May 1984

Revised: 18 March 1985

Published: 1 November 1986