On σ‐Normal  C *‐Algebras | Zendy

Saitô Kazuyuki | Zendy

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On σ‐Normal C *‐Algebras

Author(s) -

Saitô Kazuyuki

Publication year - 1997

Publication title -

bulletin of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.396

H-Index - 48

eISSN - 1469-2120

pISSN - 0024-6093

DOI - 10.1112/s0024609396002809

Subject(s) - mathematics , converse , monotone polygon , mathematics subject classification , infimum and supremum , pure mathematics , type (biology) , space (punctuation) , sequence (biology) , algebra over a field , discrete mathematics , combinatorics , ecology , linguistics , philosophy , genetics , geometry , biology

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 A h of all hermitian elements of A has a supremum in A h . 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 ]. 1991 Mathematics Subject Classification 46L05, 46L06.

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