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Completely positive maps on Coxeter groups and the ultracontractivity of the $$q$$-Ornstein-Uhlenbeck semigroup. (English) Zbl 0948.47040
Alicki, Robert (ed.) et al., Quantum probability. Workshop, Gdańsk, Poland, July 1-6, 1997. Warsaw: Polish Academy of Sciences, Institute of Mathematics, Banach Cent. Publ. 43, 87-93 (1998).
The paper contains a review of applications of a theorem concerning completely positive maps in a Hilbert space. The proofs are omitted; of course, a large list of references is presented.
For the entire collection see [Zbl 0903.00097].

##### MSC:
 47B65 Positive linear operators and order-bounded operators 47D06 One-parameter semigroups and linear evolution equations 46L51 Noncommutative measure and integration 51F15 Reflection groups, reflection geometries 20F55 Reflection and Coxeter groups (group-theoretic aspects)
##### Keywords:
completely positive maps