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Normal AW*-algebras

Published online by Cambridge University Press:  14 November 2011

J. D. Maitland Wright
J. D. Maitland Wright
Affiliation:
Department of Mathematics, University of Reading
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Synopsis

In recent years it has become clear that AW*-algebras can be much more pathological and unlike von Neumann algebras than was originally expected. When AW*-algebras are monotone complete, then the work of Kadison and Pederson shows that a particularly smooth and elegant theory can be developed. A technically weaker requirement on an AW*-algebra is that it be “normal”. This condition, which says that the lattice of projections is embedded in a well-behaved way in the partially ordered set of all self-adjoint elements, can sometimes be used as a substitute for monotone completeness. In this note we prove that when an AW*-algebra is of finite type (that is x*x = 1 implies xx* = 1) then it is normal.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 85 , Issue 1-2 , 1980 , pp. 137 - 141
Copyright
Copyright © Royal Society of Edinburgh 1980

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