## B. Tsirelson | ## On automorphisms of type II Arveson systems (probabilistic approach) | ## Recent works |

Boris Tsirelson,

"On automorphisms of type II Arveson systems (probabilistic approach)."

New York Journal of Mathematics **14**, 539-576 (2008).

Available online (free of charge) on the journal site:

http://nyjm.albany.edu/j/2008/14-25.html

See also
arXiv.org/abs/math.OA/0411062/

A research paper, 38 pages, bibl. 13 refs.

We give a counterexample to the conjecture that the automorphisms of an arbitrary Arveson system act transitively on its normalized units.

- Introduction.
- Definitions, basic observations, and the result formulated.
- Extensions of automorphisms and isomorphisms of extensions.
- Toy models: Hilbert spaces.
- Toy models: probability spaces.
- Binary extensions: probability spaces.
- Binary extensions: Hilbert spaces.
- Products of binary extensions.
- Some necessary conditions of isomorphism.
- A binary extension of Brownian motion.
- A new noise extending the white noise.
- The binary extension inside the new noise.

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