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

Hermann Pfitzner (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

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.

Domaines: Analyse fonctionnelle [math.FA]

Hermann Pfitzner. Perturbation of $l^1$-copies and measure convergence in preduals of von Neumann algebras. Journal of Operator Theory, 2002, 47, pp.145-167. ⟨hal-00131644⟩