### 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 |
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Pages (from-to) | 31-40 |

Number of pages | 9 |

Journal | Quarterly Journal of Mathematics |

Volume | 55 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2004 |

## Cite this

Brooks, J. K., Saito, K., & Wright, J. D. M. (2004). When absolute continuity on

*C**-algebras is automatically uniform.*Quarterly Journal of Mathematics*,*55*(1), 31-40. https://doi.org/10.1093/qmath/hag037