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).