Abstract:
We prove the analog of Nelson's optimal hypercontractivity inequality, for the free second quantization (in the sense of Voiculescu) of a contraction between two real Hilbert spaces. The proof extends also to the case of the q-quantization functors of Bozejko, Kümmerer and Speicher, for , interpolating between the bosonic and the fermionic functors which correspond to and respectively.
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Received: 23 July 1996 / Accepted: 29 August 1996
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Biane, P. Free Hypercontractivity . Comm Math Phys 184, 457–474 (1997). https://doi.org/10.1007/s002200050068
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DOI: https://doi.org/10.1007/s002200050068