When absolute continuity on C*-algebras is automatically uniform

J. K. Brooks, Kazuyuki Saito, John David Maitland Wright

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Let A be a C*-algebra and let K be a relatively weakly compact subset of the dual of A. Let psi be a positive linear functional on A such that, for each phi in K, phi is strongly absolutely continuous with respect to psi. Then, for each epsilon > 0, there exists delta > 0, such that for each x in the closed unit ball of A, psi (xx* + x*x) 1/2_less than or equal to delta implies \phi(x)\ less than or equal to epsilon for every phi is an element of K. This result is extended to the situation where K is a sigma-bounded set of weakly compact operators from A to a Banach space Y.

Original languageEnglish
Pages (from-to)31-40
Number of pages9
JournalQuarterly Journal of Mathematics
Volume55
Issue number1
DOIs
Publication statusPublished - 2004

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