Intersections of M-ideals and G-spaces

Åsvald Lima, G. H. Olsen and U. Uttersrud

Vol. 104 (1983), No. 1, 175–177

DOI: 10.2140/pjm.1983.104.175

Abstract

A closed subspace N of a Banach space V is called an L-summand if there is a closed subspace N′ of V such that V is the 1₁-direct sum of N and N′. A closed subspace N of V is called an M-ideal if its annihilator N^⊥ in V ^∗ is an L-summand. Among the predual L₁-spaces the G-spaces are characterized by the property that every point in the w^∗-closure of the extreme points of the dual unit ball is a multiple of an extreme point. In this note we prove that if V is a separable predual L₁-space such that the intersection of any family of M-ideals is an M-ideal, then V is a G-space.

Mathematical Subject Classification 2000

Primary: 46B20

Secondary: 46A55

Milestones

Received: 10 February 1981

Published: 1 January 1983