Strong hypercontractivity in non-commutative holomorphic spaces

Details Strong hypercontractivity in non-commutative holomorphic spaces Strong hypercontractivity in non-commutative holomorphic spaces

2004-10-25

arxiv.org/abs/math/0410534v2

Commun. Math. Phys. 259 (2005), no. 3, 615 - 637

Mathematics

Operator Algebras

25 pages, uses package xy

Scientific paper

10.1007/s00220-005-1379-5

We introduce holomorphic algebras $H_q$ in the context of the q-Gaussian
algebra $\Gamma_q$ of Bozejko, K\"ummerer, and Speicher, and give a
q-Segal-Bargmann transform for them. We then prove a strong hypercontractivity
theorem, generalizing Janson's strong (holomorphic) hypercontractivity, from
$L^2(H_q) \to L^r(H_q)$ for r an even integer.

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