# 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 language English 31-40 9 Quarterly Journal of Mathematics 55 1 https://doi.org/10.1093/qmath/hag037 Published - 2004

### Cite this

When absolute continuity on C*-algebras is automatically uniform. / Brooks, J. K.; Saito, Kazuyuki; Wright, John David Maitland.

In: Quarterly Journal of Mathematics, Vol. 55, No. 1, 2004, p. 31-40.

Research output: Contribution to journalArticle

Brooks, J. K. ; Saito, Kazuyuki ; Wright, John David Maitland. / When absolute continuity on C*-algebras is automatically uniform. In: Quarterly Journal of Mathematics. 2004 ; Vol. 55, No. 1. pp. 31-40.
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