The alternative Dunford-Pettis Property in the predual of a von Neumann algebra

Miguel Martín, and Antonio M. Peralta. "The alternative Dunford-Pettis Property in the predual of a von Neumann algebra." Studia Mathematica 147.2 (2001): 197-200. <http://eudml.org/doc/284596>.

@article{MiguelMartín2001,
abstract = {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].},
author = {Miguel Martín, Antonio M. Peralta},
journal = {Studia Mathematica},
keywords = {predual; alternative Dunford-Pettis property; W-algebra},
language = {eng},
number = {2},
pages = {197-200},
title = {The alternative Dunford-Pettis Property in the predual of a von Neumann algebra},
url = {http://eudml.org/doc/284596},
volume = {147},
year = {2001},
}

TY - JOUR
AU - Miguel Martín
AU - Antonio M. Peralta
TI - The alternative Dunford-Pettis Property in the predual of a von Neumann algebra
JO - Studia Mathematica
PY - 2001
VL - 147
IS - 2
SP - 197
EP - 200
AB - 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].
LA - eng
KW - predual; alternative Dunford-Pettis property; W-algebra
UR - http://eudml.org/doc/284596
ER -