International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 713563, 33 pages
Research Article

Extension of Spectral Scales to Unbounded Operators

Department of Mathematics, Weber State University, Ogden, UT 84404, USA

Received 30 May 2010; Accepted 14 June 2010

Academic Editor: Palle E. Jorgensen

Copyright © 2010 M. D. Wills. 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.


We extend the notion of a spectral scale to n-tuples of unbounded operators affiliated with a finite von Neumann Algebra. We focus primarily on the single-variable case and show that many of the results from the bounded theory go through in the unbounded situation. We present the currently available material on the unbounded multivariable situation. Sufficient conditions for a set to be a spectral scale are established. The relationship between convergence of operators and the convergence of the corresponding spectral scales is investigated. We establish a connection between the Akemann et al. spectral scale (1999) and that of Petz (1985).