Published May 1, 1984
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The space of extended orthomorphisms in a Riesz space
- Creators
- DePagter, B.
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.
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.).Files
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- 600
- Resolver ID
- CaltechAUTHORS:DEPpjm84
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