Homomorphisms of Riesz spaces

Charles Thomas Tucker, II

Vol. 55 (1974), No. 1, 289–300

DOI: 10.2140/pjm.1974.55.289

Abstract

If L is a Riesz space (lattice ordered vector space), a Riesz homomorphism of L is an order preserving linear map which preserves the finite operations “∨” and “∧”. It is shown here that if L is one of a large class of spaces and φ is a Riesz homomorphism from L onto an Archimedean Riesz space, then ω preserves the order limits of sequences.

Mathematical Subject Classification

Primary: 06A65

Milestones

Received: 5 March 1973

Published: 1 November 1974