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

J. K. Brooks; Kazuyuki Saito; John David Maitland Wright

doi:10.1016/S0022-247X(02)00396-7

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

J. K. Brooks, Kazuyuki Saito, John David Maitland Wright

Mathematical Science

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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
Pages (from-to)	160-167
Number of pages	7
Journal	Journal of Mathematical Analysis and Applications
Volume	276
DOIs	https://doi.org/10.1016/S0022-247X(02)00396-7
Publication status	Published - 2002

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title = "A bounded sequence of normal functionals has a subsequence which is nearly weakly convergent",

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.",

author = "Brooks, {J. K.} and Kazuyuki Saito and Wright, {John David Maitland}",

year = "2002",

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language = "English",

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journal = "Journal of Mathematical Analysis and Applications",

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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

SN - 0022-247X

VL - 276

SP - 160

EP - 167

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

ER -

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

Abstract

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