JEDNOSTKA NAUKOWA KATEGORII A+

# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

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

### Tom 147 / 2001

Studia Mathematica 147 (2001), 197-200 MSC: 46L05, 46L10. DOI: 10.4064/sm147-2-7

#### Streszczenie

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 $(\varphi _{n})$ converging weakly to $\varphi$ in $A_{*}$ with $\| \varphi _{n}\| =\| \varphi \| =1$ for all $n\in {\mathbb N}$ and a weakly null sequence $(x_{n})$ in $A$ such that $\varphi _{n} (x_{n}) \nrightarrow 0$. This answers a question posed in [7].

#### Autorzy

• Miguel MartínDepartamento de Análisis Matemático
e-mail
• Antonio M. PeraltaDepartamento de Análisis Matemático