Vol. 104, No. 1, 1983

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Intersections of M-ideals and G-spaces

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

Vol. 104 (1983), No. 1, 175–177

A closed subspace N of a Banach space V is called an L-summand if there is a closed subspace Nof 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
Received: 10 February 1981
Published: 1 January 1983
Åsvald Lima
G. H. Olsen
U. Uttersrud