Abstract
In this note, we give complete descriptions of the structure of the monotone product of two von Neumann algebras and two C*-algebras. We show that the monotone product of two simple von Neumann algebras and C*-algebras aren’t simple again. We also show that the monotone product of two hyperfinite von Neumann algebras is again hyperfinite and determine the type of the monotone product of two factors.
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