Absolute continuity on C*-algebras

Kazuyuki Saito, J D Maitland Wright

Research output: Contribution to journalArticle

Abstract

In an earlier work the notion of absolute continuity was extended from finitely additive measures to non-commutative C*-algebras. But to obtain a generalisation of the Vitali–Hahn–Saks theorem valid for all C*-algebras it was necessary to introduce ‘weak’ and ‘strong’ absolute continuity. For commutative algebras, these two notions of absolute continuity coincide but, given recent work by Chetcuti and Hamhalter, it is reasonable to ask if there are wider classes of C*-algebras for which weak and strong absolute continuity coincide.We show here that this is not true. If weak and strong absolute continuity coincide for a given algebra then the algebra must be commutative.
Original languageEnglish
Pages (from-to)135-140
Number of pages6
JournalQuarterly Journal of Mathematics
Volume61
Issue number1
Early online date14 Nov 2008
DOIs
Publication statusPublished - Mar 2010

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