### Abstract

Let B be a monotone sigma-complete C*-algebra. Let (mu(n)) (n = 1, 2,...) be a sequence in the dual of B such that lim mu(n) (p) exists for each projection p. We prove that the sequence must converge weakly. As an application, we obtain a non-commutative generalisation of the Brooks-Jewett Theorem. (C) 2004 Elsevier Inc. All rights reserved.

Original language | English |
---|---|

Pages (from-to) | 141-146 |

Number of pages | 5 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 294 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2004 |

### Cite this

*C**-algebra.

*Journal of Mathematical Analysis and Applications*,

*294*(1), 141-146. https://doi.org/10.1016/j.jmaa.2004.02.004

**Convergence in the dual of a s-complete C*-algebra.** / Brooks, J. K.; Wright, John David Maitland.

Research output: Contribution to journal › Article

*C**-algebra',

*Journal of Mathematical Analysis and Applications*, vol. 294, no. 1, pp. 141-146. https://doi.org/10.1016/j.jmaa.2004.02.004

*C**-algebra. Journal of Mathematical Analysis and Applications. 2004;294(1):141-146. https://doi.org/10.1016/j.jmaa.2004.02.004

}

TY - JOUR

T1 - Convergence in the dual of a s-complete C*-algebra

AU - Brooks, J. K.

AU - Wright, John David Maitland

PY - 2004

Y1 - 2004

N2 - Let B be a monotone sigma-complete C*-algebra. Let (mu(n)) (n = 1, 2,...) be a sequence in the dual of B such that lim mu(n) (p) exists for each projection p. We prove that the sequence must converge weakly. As an application, we obtain a non-commutative generalisation of the Brooks-Jewett Theorem. (C) 2004 Elsevier Inc. All rights reserved.

AB - Let B be a monotone sigma-complete C*-algebra. Let (mu(n)) (n = 1, 2,...) be a sequence in the dual of B such that lim mu(n) (p) exists for each projection p. We prove that the sequence must converge weakly. As an application, we obtain a non-commutative generalisation of the Brooks-Jewett Theorem. (C) 2004 Elsevier Inc. All rights reserved.

U2 - 10.1016/j.jmaa.2004.02.004

DO - 10.1016/j.jmaa.2004.02.004

M3 - Article

VL - 294

SP - 141

EP - 146

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 1

ER -