This article is cited in 2 papers

Noncommutative integration for traces with values in Kantorovich–Pinsker spaces

B. S. Zakirov^a, V. I. Chilin<sup>b

a</sup> Chair of Higher Mathematics, Tashkent Railway Engineering Institute, Tashkent, Republic of Uzbekistan
^b Chair of Algebra and Function Analysis, National University of Uzbekistan, Tashkent, Republic of Uzbekistan

Abstract: In this paper we consider traces on von Neumann algebras with values in complex Kantorovich–Pinsker spaces. We establish the connection between the convergence with respect to the trace and the convergence locally in measure in the algebra $S(M)$ of measurable operators affiliated with $M$. We define the $(bo)$-complete lattice-normed spaces of integrable operators in $S(M)$ and prove that they are decomposable if the trace possesses the Maharam property.

Keywords: von Neumann algebra, measurable operator, convergence locally in measure, vector-valued trace, Banach–Kantorovich space.

UDC: 517.98

Received: 21.01.2009

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:10, 15–26

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