Perturbation of $l^1$-copies and measure convergence in preduals of von Neumann algebras

Details Perturbation of $l^1$-copies and measure convergence in preduals of von Neumann algebras Perturbation of $l^1$-copies and measure convergence in preduals of von Neumann algebras

2000-03-24

arxiv.org/abs/math/0003152v1

Mathematics

Functional Analysis

submitted to J. of Op. Th

Scientific paper

Let L_1 be the predual of a von Neumann algebra with a finite faithful normal trace. We show that a bounded sequence in L_1 converges to 0 in measure if and only if each of its subsequences admits another subsequence which converges to 0 in norm or spans $l^1$ "almost isometrically". Furthermore we give a quantitative version of an essentially known result concerning the perturbation of a sequence spanning $l^1$ isomorphically in the dual of a C$^*$-algebra.

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