B. Tsirelson

Subproduct systems of Hilbert spaces: dimension two

Recent works

Boris Tsirelson,
"Subproduct systems of Hilbert spaces: dimension two."
arXiv:0906.4255.
Available online (free of charge) from e-print archive (USA):
arXiv.org/abs/0906.4255/
or its Israeli mirror:
il.arXiv.org/abs/0906.4255/


A research eprint, 16 pages, bibl. 6 refs.

A subproduct system of two-dimensional Hilbert spaces can generate an Arveson system of type I1 only. All possible cases are classified up to isomorphism. This work is triggered by a question of Bhat: can a subproduct system of n-dimensional Hilbert spaces generate an Arveson system of type II or III ? The question is still open for n>2.

  1. Discrete time.
  2. Time on a sublattice.
  3. Rational time.
  4. Arveson systems, Liebscher continuity.
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