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 |
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| 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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