On the Dunford-Pettis property of function modules of abstract L-spaces

Gerhard Gierz

Vol. 121 (1986), No. 1, 73–82

DOI: 10.2140/pjm.1986.121.73

Abstract

The main result of this note states that a function module of Banach spaces has the Dunford-Pettis Property, provided that all summands are spaces of the form L₁(μ). As a corollary we obtain that every injective Banach lattice has the Dunford-Pettis Property. Another corollary states that certain spaces of compact operators have the Dunford-Pettis Property.

Mathematical Subject Classification 2000

Primary: 46E40

Secondary: 46B20, 46M20

Milestones

Received: 2 August 1984

Revised: 28 December 1984

Published: 1 January 1986