Intermediate Riesz spaces

Joseph E. Quinn

Vol. 56 (1975), No. 1, 225–263

DOI: 10.2140/pjm.1975.56.225

Abstract

A Riesz space E will be defined to be intermediate with respect to the Riesz space L if L can be embedded in E as a Riesz subspace L^∗ in such a way that the elements of E are both the infimum and the supremum of elements in L^#. The main objectives of this paper are to investigate the extendability of certain order convergence properties from a Riesz space to its intermediate spaces and to compare the prime ideal structure of a Riesz space to the prime ideal structure of its intermediate spaces.

Mathematical Subject Classification 2000

Primary: 46A40

Secondary: 06A65

Milestones

Received: 22 July 1973

Revised: 18 April 1974

Published: 1 January 1975