Is there any analog of studying spectral properties of automorphisms of von Neumann algebra? Does it make sense, if anybody knows please give a reference.
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$\begingroup$ An analog in what? $\endgroup$– YCorCommented Mar 29, 2019 at 9:09
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$\begingroup$ Studying spectral properties and spectral measures $\endgroup$– user136400Commented Mar 29, 2019 at 9:13
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1$\begingroup$ Well, the original setting is spectral properties and spectral measures, and you want an analogue for automorphisms of von Neumann algebras, if I understand correctly (this is not clear at all in the question). $\endgroup$– YCorCommented Mar 29, 2019 at 10:20
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I'm not really sure what you are asking, but is the following of interest:
https://mathscinet.ams.org/mathscinet-getitem?mr=348518 https://www.sciencedirect.com/science/article/pii/0022123674900342
Arveson, William
On groups of automorphisms of operator algebras.
J. Functional Analysis 15 (1974), 217–243.
Arveson develops a notion of "spectral subspaces" for automorphisms (or more generally, one-parameter groups of isometries on Banach spaces). The details are somewhat technical, but the paper is an easy read.
answered Mar 29, 2019 at 8:37