A decomposition theorem in II_1-factors
arXiv:1302.1114
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.
16 pages. Version 2 differs from version 1 in that it contains more explanation of a few points and the statements of results are broadened apply to diffuse, finite von Neumann algebras rather than just II_1-factors