Short communications

The predual space of a $\mathrm{JBW}^*$-triple

A. A. Rakhimov

The Tashkent Automobile and Road Construction Institute, 20 Amir Temur St., Tashkent, Uzbekistan

Abstract: In the paper $\mathrm{JB}^*$-triples which are dual Banach spaces are considered as analogues of $\mathrm{JBW}^*$-algebras. For $\mathrm{JBW}^*$-triples an analogue of the classical theorem of Vitali–Hahn–Saks on convergent sequences of measures and a theorem on weak compactness of a set of normal functionals are proved.

Keywords and phrases: von Neumann algebra, $\mathrm{JBW}^*$-triple, normal functionals.

UDC: 17C65, 46H70, 46L10, 46L70

Received: 17.01.2013

Language: English