2000/03/24 by Hermann Pfitzner, Pfitzner, Hermann
Mathematics · #46B20 #46L05 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B20 #msc:46L05
paper · pdf · doi:10.48550/arxiv.math/0003152
submitted to J. of Op. Th
arxiv created 2000/03/24 · arxiv updated 2009/11/30
Let L1 be the predual of a von Neumann algebra with a finite faithful normal trace. We show that a bounded sequence in L1 converges to 0 in measure if and only if each of its subsequences admits another subsequence which converges to 0 in norm or spans l1 "almost isometrically". Furthermore we give a quantitative version of an essentially known result concerning the perturbation of a sequence spanning l1 isomorphically in the dual of a C^*-algebra.