A decomposition theorem in II_1-factors
Operator Algebras
2013-06-17 v2 Functional Analysis
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.
Cite
@article{arxiv.1302.1114,
title = {A decomposition theorem in II_1-factors},
author = {K. Dykema and F. Sukochev and D. Zanin},
journal= {arXiv preprint arXiv:1302.1114},
year = {2013}
}
Comments
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