Extension of spectral scales to unbounded operators (Q1958081)

Summary: 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 carry over to the unbounded case. 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 \textit{C.\,A.\thinspace Akemann, J.\,Anderson} and \textit{N.\,Weaver}'s spectral scale [J.~Funct.\ Anal.\ 165, No.\,2, 258--292 (1999; Zbl 0937.47003)] and that of \textit{D.\,Petz} [J.~Math.\ Anal.\ Appl.\ 109, 74--82 (1985; Zbl 0655.47032)].