Injective Banach lattices with strong order units

Gerhard Gierz

Vol. 110 (1984), No. 2, 297–305

DOI: 10.2140/pjm.1984.110.297

Abstract

In this note it is shown that a Banach lattice with a strong order unit is injective (i.e. has the Hahn-Banach extension property for positive linear operators) if and only if E is a finite m-sum of spaces of the form C(X,l₁ⁿ), where X is compact and extremally disconnected and where l₁ⁿ denotes Rⁿ with the L-norm.

Mathematical Subject Classification

Primary: 46B30, 46B30

Milestones

Received: 3 May 1982

Published: 1 February 1984