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Fractional powers on noncommutative L p for p < 1

Abstract : We prove that the homogeneous functional calculus associated to x → |x| θ or x → sgn (x)|x| θ for 0 < θ < 1 is θ-Hölder on selfadjoint elements of noncommutative Lp-spaces for 0 < p ∞ with values in L p/θ. This extends an inequality of Birman, Koplienko and Solomjak also obtained by Ando.
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Submitted on : Monday, June 18, 2018 - 1:07:41 PM
Last modification on : Monday, April 27, 2020 - 4:14:03 PM
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Éric Ricard. Fractional powers on noncommutative L p for p < 1. Advances in Mathematics, Elsevier, 2018, 333, pp.194-211. ⟨10.1016/j.aim.2018.05.024⟩. ⟨hal-01817762⟩

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