## Abstract

Several results in noncommutative measure theory for C^{*}-algebras are proved. A bounded linear map from a C^{*}-algebra to a weakly sequentially complete Banach space is weakly compact (Theorem 4.2). This was a conjecture of Sakai. This result is a consequence of a recent theorem of Pedersen. A theorem of the Vitali-Hahn-Saks type states that a sequence {f{hook}_{i}} of states on a W^{*}-algebra converges weakly if it converges weak^{*} (Corollary 3.3).

Original language | English |
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Pages (from-to) | 446-450 |

Number of pages | 5 |

Journal | Journal of Functional Analysis |

Volume | 10 |

Issue number | 4 |

DOIs | |

Publication status | Published - Aug 1972 |

### Bibliographical note

Funding Information:*Partially supported by NSF grant GP 19101. + Supported in part by NRC grant A 7552.

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