International Journal of Mathematics and Mathematical Sciences
Volume 2011 (2011), Article ID 789182, 24 pages
http://dx.doi.org/10.1155/2011/789182
Research Article

The Spectral Scale of a Self-Adjoint Operator in a Semifinite von Neumann Algebra

Christopher M. Pavone

Department of Mathematics and Statistics, California State University, Chico, 400 West First Street, Chico, CA 95928-0525, USA

Received 1 November 2010; Revised 10 March 2011; Accepted 11 March 2011

Academic Editor: Ilya M. Spitkovsky

Copyright © 2011 Christopher M. Pavone. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We extend Akemann, Anderson, and Weaver's Spectral Scale definition to include selfadjoint operators from semifinite von Neumann algebras. New illustrations of spectral scales in both the finite and semifinite von Neumann settings are presented. A counterexample to a conjecture made by Akemann concerning normal operators and the geometry of the their perspective spectral scales (in the finite setting) is offered.