Hypercontractivity in Non-commutative Holomorphic Spaces
نویسنده
چکیده
We prove an analog of Janson’s strong hypercontractivity inequality in a class of non-commutative “holomorphic” algebras. Our setting is the q-Gaussian algebras Γq associated to the q-Fock spaces of Bozejko, Kümmerer and Speicher, for q ∈ [−1, 1]. We construct subalgebras Hq ⊂ Γq , a q-Segal-Bargmann transform, and prove Janson’s strong hypercontractivity L(Hq)→ L(Hq) for r an even integer.
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