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

Abstract

The von-Neumann algebras whose predual has the Dunford-Pettis property are characterised as being Type I finite. This answers the question asked by Chu and Iochum in <italic>The Dunford Pettis property in</italic> <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper C Superscript asterisk"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mi>C</mml:mi> <mml:mo>∗<!-- ∗ --></mml:mo> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{C^*}</mml:annotation> </mml:semantics> </mml:math> </inline-formula><italic>-algebras</italic>, Studia Math. <bold>97</bold> (1990), 59-64.