Noncommutative integration for traces with values in Kantorovich-Pinsker spaces

In this paper we consider traces on a von Neumann algebra M 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.

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