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.



Analogue of spectral values of automorphisms in vN algebra
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.


