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.
|Number of pages||7|
|Journal||Journal of Mathematical Analysis and Applications|
|Publication status||Published - 2002|