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A decomposition theorem in II_1-factors (1302.1114v2)
Published 5 Feb 2013 in math.OA and math.FA
Abstract: Building on results of Haagerup and Schultz, we decompose an arbitrary operator in a diffuse, finite von Neumann algebra into the sum of a normal operator and an s.o.t.-quasinilpotent operator. We also prove an analogue of Weyl's inequality relating eigenvalues and singular values for operators in a diffuse, finite von Neumann algebra.