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Majorization, interpolation and noncommutative Khinchin inequalities

Volume 258 / 2021

Léonard Cadilhac Studia Mathematica 258 (2021), 1-26 MSC: Primary 46B70; Secondary 46L52. DOI: 10.4064/sm181217-30-1 Published online: 4 November 2020

Abstract

Let $0 \lt p \lt q\leq \infty $ and $\alpha \in (0,\infty ]$. We give a characterization of quasi-Banach interpolation spaces for the couple $(L_p(0,\alpha ),L_q(0,\alpha ))$ in terms of two monotonicity properties, extending known results which mainly dealt with Banach spaces. This enables us to recover recent results of Cwikel and Nilsson on sequence spaces and to solve a conjecture of Levitina, Sukochev and Zanin in the setting of function spaces. We apply the results obtained to characterize symmetric spaces in which the standard forms of the noncommutative Khinchin inequalities hold.

Authors

  • Léonard CadilhacInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland
    and
    Normandie Univ, Unicaen, CNRS
    Laboratoire de Mathématiques Nicolas Oresme
    14000 Caen, France
    e-mail

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