Generalized notion of a trace for von Neumann algebras
Botir ZakirovTashkent Institute of Railway Transport Engineers, Tashkent, 100167, Uzbekistan
ABI
Abstract
On a von Neumann algebra M, we consider traces with values in the algebra L 0 of measurable complex-valued functions. We show that every faithful normal L 0-valued trace on M generates an L 0-valued metric on the algebra of measurable operators that are affiliated with M. Moreover, convergence in this metric coincides with local convergence in measure.
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