# On some groups of automorphisms of von Neumann algebras with cyclic and separating vector

##### Citations

103 citations

### Cites background from "On some groups of automorphisms of ..."

...12 in [5]), the spectrum of the Liouvillean of an ergodic quantum dynamical system is not arbitrary (see [24] and [31] for related results)....

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94 citations

### Cites background from "On some groups of automorphisms of ..."

...They made it clear that the analysis of algebraic properties of quantum system can be based on the study of spectral properties of the Liouvillean (although these ideas can be traced to earlier works, such as [ Ja ])....

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73 citations

### Cites background from "On some groups of automorphisms of ..."

...From part (vi) of the corollary to Theorem 5 above, we see that all the conditions of Theorem 3.2 in [ 12 ] now hold for every generalized K-flow, so that (i) is thus established....

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60 citations

### Cites methods or result from "On some groups of automorphisms of ..."

...In this paper we turn to the question of automorphism groups of avon Neumann algebra M which commute with the modular automorphism group associated with a given normal state on M. This situation has been considered, for example in [15] and [ 8 ]....

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...Jadcyck [ 8 ] has obtained the part of this theorem concerning the fixed points of {Ug:g~{¢} by a different method....

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...Added in proof: Professor Stormer, in a private discussion with the second author, has pointed out that Jadczyk's method [ 8 ] extends to give a simpler proof of the Theorem...

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...Results obtained here extend those in [15] and [ 8 ]....

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...We extend here results of [15] and [ 8 ] concerning the discrete spectrum of certain abelian unitary groups whose induced automorphism group commutes with the modular automorphism group....

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43 citations

### Cites background from "On some groups of automorphisms of ..."

...Lemma 4.5. Let co ~ I~(1I) be separating then P~ = P~. The proof can be found in [ 15 ], Lemma 2.2....

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