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Extensions of orthomorphisms

Published online by Cambridge University Press:  09 April 2009

A. W. Wickstead
A. W. Wickstead
Affiliation:
Department of Pure Mathematics The Queen's University of BelfastBT7 INN Northern, Ireland
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Abstract

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We consider, on an Archimedean Riesz space, the spaces of all linear operators lying between two multiples of the identity (for the order), those leaving all ideals invariant and the order bounded orthomorphisms. We find, if E is uniformly complete, necessary and sufficient conditions for all such operators defined on sublattices of E to extend to the whole of E. Examples are given to show the role of uniform completeness. For the space of all orthomorphisms we give a sufficient condition on E for such an extension to exist.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 29 , Issue 1 , February 1980 , pp. 87 - 98
Copyright
Copyright © Australian Mathematical Society 1980

References

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