Let A be a type II von Neumann algebra with predual A⁎. We prove that A⁎ does not have the alternative Dunford-Pettis property introduced by W. Freedman [7], i.e., there is a sequence (φₙ) converging weakly to φ in A⁎ with ||φₙ|| = ||φ|| = 1 for all n ∈ ℕ and a weakly null sequence (xₙ) in A such that φₙ(xₙ) ↛ 0. This answers a question posed in [7].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-2-7,
author = {Miguel Mart\'\i n and Antonio M. Peralta},
title = {The alternative Dunford-Pettis Property in the predual of a von Neumann algebra},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {197-200},
zbl = {0998.46028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-2-7}
}
Miguel Martín; Antonio M. Peralta. The alternative Dunford-Pettis Property in the predual of a von Neumann algebra. Studia Mathematica, Tome 147 (2001) pp. 197-200. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm147-2-7/