Countably additive homomorphisms between von Neumann algebras

Authors:
L. J. Bunce and J. Hamhalter

Journal:
Proc. Amer. Math. Soc. **123** (1995), 3437-3441

MSC:
Primary 46L50

DOI:
https://doi.org/10.1090/S0002-9939-1995-1285978-7

MathSciNet review:
1285978

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Abstract: Let *M* and *N* be von Neumann algebras where *M* has no abelian direct summand. A -homomorphism is said to be countably additive if , for every sequence of orthogonal projections in *M*. We prove that a -homomorphism is countably additive if and only if for every pair of projections *e* and *f* of *M*. A corollary is that if, in addition, *M* has no Type direct summands, then every lattice morphism from the projections of *M* into the projections of *N* is a -lattice morphism.

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DOI:
https://doi.org/10.1090/S0002-9939-1995-1285978-7

Article copyright:
© Copyright 1995
American Mathematical Society