### Abstract

Let (phi(n)) be a norm bounded sequence in the pre-dual of a von Neumann algebra M. In general it is not true that this sequence has a weakly convergent subsequence. But given a normal state psi, then, for any epsilon > 0, there exists a projection e such that psi (1 - e) less than or equal to epsilon and the restriction of (phi(n)) to eMe has a subsequence which converges weakly to a normal functional on eMe. (C) 2002 Elsevier Science (USA). All rights reserved.

Original language | English |
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Pages (from-to) | 160-167 |

Number of pages | 7 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 276 |

DOIs | |

Publication status | Published - 2002 |

### Cite this

*Journal of Mathematical Analysis and Applications*,

*276*, 160-167. https://doi.org/10.1016/S0022-247X(02)00396-7

**A bounded sequence of normal functionals has a subsequence which is nearly weakly convergent.** / Brooks, J. K.; Saito, Kazuyuki; Wright, John David Maitland.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 276, pp. 160-167. https://doi.org/10.1016/S0022-247X(02)00396-7

}

TY - JOUR

T1 - A bounded sequence of normal functionals has a subsequence which is nearly weakly convergent

AU - Brooks, J. K.

AU - Saito, Kazuyuki

AU - Wright, John David Maitland

PY - 2002

Y1 - 2002

N2 - Let (phi(n)) be a norm bounded sequence in the pre-dual of a von Neumann algebra M. In general it is not true that this sequence has a weakly convergent subsequence. But given a normal state psi, then, for any epsilon > 0, there exists a projection e such that psi (1 - e) less than or equal to epsilon and the restriction of (phi(n)) to eMe has a subsequence which converges weakly to a normal functional on eMe. (C) 2002 Elsevier Science (USA). All rights reserved.

AB - Let (phi(n)) be a norm bounded sequence in the pre-dual of a von Neumann algebra M. In general it is not true that this sequence has a weakly convergent subsequence. But given a normal state psi, then, for any epsilon > 0, there exists a projection e such that psi (1 - e) less than or equal to epsilon and the restriction of (phi(n)) to eMe has a subsequence which converges weakly to a normal functional on eMe. (C) 2002 Elsevier Science (USA). All rights reserved.

U2 - 10.1016/S0022-247X(02)00396-7

DO - 10.1016/S0022-247X(02)00396-7

M3 - Article

VL - 276

SP - 160

EP - 167

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

ER -