Orthomorphisms of a Commutative W*-algebra

P. G. Dodds

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1 Citation (Scopus)


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 ReM 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 ReM, and via the vector lattice Radon-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.

Original languageEnglish
Pages (from-to)143-168
Number of pages26
JournalJournal of the Australian Mathematical Society
Issue number2
Publication statusPublished - Oct 1984


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