The space of extended orthomorphisms in a Riesz space

Bernardus de Pagter

Vol. 112 (1984), No. 1, 193–210

DOI: 10.2140/pjm.1984.112.193

Abstract

We study the space Orth^∞(L) of extended orthomorphisms in an Archimedean Riesz space L and its analogies with the complete ring of quotients of a commutative ring with unit element. It is shown that for any uniformly complete f-algebra A with unit element, Orth^∞(A) is isomorphic with the complete ring of quotients of A. Furthermore, it is proved that for any uniformly complete Riesz space L the space Orth^∞(L) is isomorphic to the lateral completion of L. Finally, it is shown that for any uniformly complete Riesz space L the ring Orth^∞(L) is von Neumann regular.

Mathematical Subject Classification 2000

Primary: 46A40

Secondary: 06F20

Milestones

Received: 17 March 1982

Revised: 27 August 1982

Published: 1 May 1984