Journal Article

When absolute continuity on C‐algebras is automatically uniform

J. K. Brooks, Kazuyuki SAITÔ and J. D. Maitland Wright

in The Quarterly Journal of Mathematics

Volume 55, issue 1, pages 31-40
Published in print March 2004 | ISSN: 0033-5606
Published online March 2004 | e-ISSN: 1464-3847 | DOI: https://dx.doi.org/10.1093/qmath/hag037
When absolute continuity on C‐algebras is automatically uniform

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Let A be a C*‐algebra and let K be a relatively weakly compact subset of the dual of A. Let ψbe a positive linear functional on A such that, for each φin K, φis strongly absolutely continuous with respect to ψ. Then, for each ε> 0, there exists δ> 0, such that for each x in the closed unit ball of A, ψ(xx* +x*x)1/2 ≤δimplies |φ(x) |≤εfor every φ∈K. This result is extended to the situation where K is a σ‐bounded set of weakly compact operators from A to a Banach space Y.

Journal Article.  0 words. 

Subjects: Pure Mathematics

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