B. Tsirelson

Non-isomorphic product systems

Recent works

Boris Tsirelson,
"Non-isomorphic product systems."
In: Advances in Quantum Dynamics (eds. G. Price et al), Contemporary Mathematics 335, AMS, pp. 273--328 (2003).
Available online (free of charge) from e-print archive (USA):
or its Israeli mirror:

A research paper, 70 pages, bibl. 16 refs.

Uncountably many mutually non-isomorphic product systems (that is, continuous tensor products of Hilbert spaces) of types II0 and III are constructed by probabilistic means (random sets and off-white noises), answering four questions of W. Arveson. Results of math.FA/0001070, math.FA/0006165 are improved, and proofs are more readable.

  1. Introduction
  2. Basic notions.
  3. Some invariants.
  4. Continuous products of measure classes.
  5. Continuous products of probability spaces.
  6. Random sets, and type II0.
  7. Constructing random sets.
  8. Time reversal.
  9. FHS space: logarithm of a Hilbert space.
  10. Continuous sums and off-white noises.
  11. Type III.
  12. The invariant via the logarithm.
  13. Ensuring asymptotic orthogonality.
  14. Calculating the invariant.
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