Geodesic
The alternative Dunford–Pettis Property in the predual of a von Neumann algebra
Miguel Martín1 ; Antonio M. Peralta1
1 Departamento de Análisis Matemático Facultad de Ciencias Universidad de Granada 18071 Granada, Spain
Studia Mathematica, Tome 147 (2001) no. 2, pp. 197-200

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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].
DOI : 10.4064/sm147-2-7
Keywords: type von neumann algebra predual * prove * does have alternative dunford pettis property introduced freedman there sequence varphi converging weakly varphi * varphi varphi mathbb weakly null sequence varphi nrightarrow answers question posed

Miguel Martín 1 ; Antonio M. Peralta 1

1 Departamento de Análisis Matemático Facultad de Ciencias Universidad de Granada 18071 Granada, Spain 
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Miguel Martín; Antonio M. Peralta. The alternative Dunford–Pettis Property in
the predual of a von Neumann algebra. Studia Mathematica, Tome 147 (2001) no. 2, pp. 197-200. doi: 10.4064/sm147-2-7

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