Extension of Spectral Scales to Unbounded Operators
2010 ◽
Vol 2010
◽
pp. 1-33
Keyword(s):
We extend the notion of a spectral scale ton-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).
1983 ◽
Vol 24
(1)
◽
pp. 71-74
◽
2007 ◽
Vol 100
(2)
◽
pp. 209
◽
2008 ◽
Vol 337
(2)
◽
pp. 1226-1237
◽
Keyword(s):
2007 ◽
Vol 140
(3)
◽
pp. 445-451
◽
2008 ◽
Vol 19
(04)
◽
pp. 481-501
◽
2018 ◽
Vol 38
(2)
◽
pp. 429-440
Keyword(s):
Keyword(s):
2019 ◽
Vol 169
(3)
◽
pp. 607-622