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

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

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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 languageEnglish
Pages (from-to)160-167
Number of pages7
JournalJournal of Mathematical Analysis and Applications
Volume276
DOIs
Publication statusPublished - 2002

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