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

Pfitzner, Hermann

HAL, hal-00131644 / Harvested from HAL

Résumé

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.

Publié le : 2002-07-05
Classification: [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA]

@article{hal-00131644,
     author = {Pfitzner, Hermann},
     title = {Perturbation of $l^1$-copies and measure convergence in preduals of von Neumann algebras},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00131644}
}

Pfitzner, Hermann. Perturbation of $l^1$-copies and measure convergence in preduals of von Neumann algebras. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00131644/