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Orthomorphisms of a commutative W*-algebra

Part of: Topological linear spaces and related structures

Published online by Cambridge University Press:  09 April 2009

P. G. Dodds
P. G. Dodds
Affiliation:
The Flinders University of South AustraliaBedford Park, S.A. 5042, Australia
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Abstract

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If M is a commutative W*-algebra of operators and if ReM is the Dedekind complete Riesz space of self-adjoint elements of M, then it is shown that the set of densely defined self-adjoint transformations affiliated with ReM is a Dedekind complete, laterally complete Riesz algebra containing ReM as an order dense ideal. The Riesz algebra of densely defined orthomorphisms on ReM is shown to coincide with , and via the vector lattice Randon-Nikodym theorem of Luxemburg and Schep, it is shown that the lateral completion of ReM may be identified with the extended order dual of ReM.

MSC classification

Secondary: 46A40: Ordered topological linear spaces, vector lattices
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 2 , October 1984 , pp. 143 - 168
Copyright
Copyright © Australian Mathematical Society 1984

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