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The space of extended orthomorphisms in a Riesz space

DePagter, B. (1984) The space of extended orthomorphisms in a Riesz space. Pacific Journal of Mathematics, 112 (1). pp. 193-210. ISSN 0030-8730. http://resolver.caltech.edu/CaltechAUTHORS:DEPpjm84

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Abstract

We study the space Orth[infinity](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[infinity](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[infinity]( L) is isomorphic to the lateral completion of L. Finally, it is shown that for any uniformly complete Riesz space L the ring Orth[infinity](L) is von Neumann regular.


Item Type:Article
Additional Information:© 1984 Pacific Journal of Mathematics. Received March 17, 1982 and in revised form August 27, 1982. Work on this paper was supported by a NATO-Science Fellowship from the Netherlands Organization for the Advancement of Pure Research (Z.W.O.).
Record Number:CaltechAUTHORS:DEPpjm84
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:DEPpjm84
Alternative URL:http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.pjm/1102710108
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:600
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:01 Sep 2005
Last Modified:26 Dec 2012 08:40

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