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Optimal Two—Uniform Convexity and Fermion Hypercontractivity

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Book cover Quantum and Non-Commutative Analysis

Part of the book series: Mathematical Physics Studies ((MPST,volume 16))

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Abstract

An optimal two-uniform convexity theorem (obtained together with K. Ball) is presented. This is shown to lead to optimal hypercontractivity bounds for the fermion oscillator semigroup, conjectured by L. Gross in 1975. These are the fermion analogs of the optimal hypercontractivity bounds for the boson oscillator semigroup obtained in 1973 by E. Nelson.

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Author information

Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, Ga., 30332, USA

    Eric A. Carlen

  2. Departments of Mathematics and Physics, Princeton University, Princeton, NJ, 08544, USA

    Elliott H. Lieb

Authors
  1. Eric A. Carlen
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  2. Elliott H. Lieb
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Editor information

Editors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, 606-01, Sakyo-ku, Kyoto, Japan

    Huzihiro Araki

  2. Department of Mathematics and Information, College of Liberal Arts, Kyoto University, Sakyo-ku, Yoshida Kyoto 606, Japan

    Keiichi R. Ito

  3. Department of Mathematics Faculty of Science, Hokkaido University, Sapporo 060, Japan

    Akitaka Kishimoto

  4. Research Institute for Mathematical Sciences, Kyoto University, 606-01, Kyoto, Japan

    Izumi Ojima

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© 1993 Springer Science+Business Media Dordrecht

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Carlen, E.A., Lieb, E.H. (1993). Optimal Two—Uniform Convexity and Fermion Hypercontractivity. In: Araki, H., Ito, K.R., Kishimoto, A., Ojima, I. (eds) Quantum and Non-Commutative Analysis. Mathematical Physics Studies, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-2823-2_7

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  • DOI: https://doi.org/10.1007/978-94-017-2823-2_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4334-4

  • Online ISBN: 978-94-017-2823-2

  • eBook Packages: Springer Book Archive

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