Vol. 69, No. 2, 1977

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 307: 1  2
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Riesz homomorphisms and positive linear maps

Charles Thomas Tucker, II

Vol. 69 (1977), No. 2, 551–556
Abstract

It was shown in previous papers [C. T. Tucker, “Homomorphisms of Riesz spaces,” Pacific J. Math., 55 (1974), 289–300, and “Concerning σ-homomorphisms of Riesz spaces,” Pacific J. Math., 57 (1975), 585–590] that there is a large class β of Riesz spaces with the property that if L belongs to β and ϕ is a Riesz homomorphism of L into an Archimedean Riesz space then ϕ preserves the order limit of sequences. In this paper it is shown that if L belongs to β then every order bounded linear map of L into an Archimedean, directed, partially ordered vector space is sequentially continuous. An application of this is made to the theory of Baire funtions. Further, some properties of those members of β which are also normed Riesz spaces are considered.

Mathematical Subject Classification 2000
Primary: 47B55, 47B55
Secondary: 46A40
Milestones
Received: 6 April 1976
Revised: 1 November 1976
Published: 1 April 1977
Authors
Charles Thomas Tucker, II