## B. Tsirelson | ## Non-isomorphic product systems | ## Recent works |

Boris Tsirelson,

"Non-isomorphic product systems."

math.FA/0210457.

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):

arXiv.org/abs/math.FA/0210457/

or its Israeli mirror:

il.arXiv.org/abs/math.FA/0210457/

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
*II*_{0} 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.

- Introduction
- Basic notions.
- Some invariants.
- Continuous products of measure classes.
- Continuous products of probability spaces.
- Random sets, and type
*II*_{0}. - Constructing random sets.
- Time reversal.
- FHS space: logarithm of a Hilbert space.
- Continuous sums and off-white noises.
- Type
*III*. - The invariant via the logarithm.
- Ensuring asymptotic orthogonality.
- Calculating the invariant.

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