Journal of Operator Theory

Volume 47, Issue 1, Winter 2002 pp. 145-167.

Perturbation of

$\leins$ -copies and measure convergence

Authors: Hermann Pfitzner
Author institution: Universite d'Orleans, BP 6759, F-45067 Orleans Cedex 2, France

Summary: Let

$\Leins$ be the predual of a von Neumann algebra with a finite faithful normal trace. We show that a bounded sequence in

$\Leins$ converges to

$0$ in measure if and only if each of its subsequences admits another subsequence which converges to

$0$ in norm or spans

$\leins$ {\it almost isometrically}. Furthermore we give a quantitative version of an essentially known result concerning the perturbation of a sequence spanning

$\leins$ isomorphically in the dual of a

$C^*$ -algebra.

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