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ON σ-NORMAL C*-ALGEBRAS

Published online by Cambridge University Press:  01 July 1997

KAZUYUKI SAITÔ
KAZUYUKI SAITÔ
Affiliation:
Mathematical Institute, Tôhoku University, Sendai, 980, Japan
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Abstract

A C*-algebra A is said to be monotone (respectively monotone σ-) complete if every increasing net (respectively increasing sequence) of elements in the ordered space Ah of all hermitian elements of A has a supremum in Ah. It is straightforward to verify that every monotone complete C*-algebra is an AW*-algebra. For type I AW*-algebras, the converse is known to be true. However, for general AW*-algebras, this question is still open, although an impressive attack on the problem was made by E. Christensen and G. K. Pedersen, who showed that properly infinite AW*-algebras are monotone σ-complete [4].

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 4 , July 1997 , pp. 480 - 482
Copyright
© The London Mathematical Society 1997

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