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On reduction theory and Brown measure for closed unbounded operators (1509.03362v1)
Published 10 Sep 2015 in math.OA
Abstract: The theory of direct integral decompositions of both bounded and unbounded operators is further developed; in particular, results about spectral projections, functional calculus and affiliation to von Neumann algebras are proved. For operators belonging to or affiliated to a tracial von Neumann algebra that is a direct integral von Neumann algebra, the Brown measure is shown to be given by the corresponding integral of Brown measures.