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:
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.

  1. Introduction.
  2. Definitions, basic observations, and the result formulated.
  3. Extensions of automorphisms and isomorphisms of extensions.
  4. Toy models: Hilbert spaces.
  5. Toy models: probability spaces.
  6. Binary extensions: probability spaces.
  7. Binary extensions: Hilbert spaces.
  8. Products of binary extensions.
  9. Some necessary conditions of isomorphism.
  10. A binary extension of Brownian motion.
  11. A new noise extending the white noise.
  12. The binary extension inside the new noise.
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