Normal Limits of Nilpotents in C*-Algebras
arXiv:1205.3537 · doi:10.7900/jot.2012nov15.1983
Abstract
We will investigate the intersection of the normal operators with the closure of the nilpotent and quasinilpotent operators in various C*-algebras. A complete characterization will be given for type I and type III von Neumann algebras with separable predual and for unital, simple, purely infinite C*-algebras. Some restrictions that prevent normal operators from being limits of quasinilpotent operators will be given. The case of AF C*-algebras will be of particular interest. In addition, the closure of the span of the nilpotent operators and the distance from a projection to the nilpotent operators of various C*-algebras will be examined.
arXiv commentVersion 3 is an update to more accurately represent what will appear in print. The von Neumann algebra results of version 2 now appear in "P. Skoufranis, Normal Limits of Nilpotent Operators in von Neumann Algebras, Integral Equations and Operator Theory 77 (2013), no. 3, 407-439.". This version will appear in the Journal of Operator Theory under the same title