Fractional powers on noncommutative L p for p < 1

Éric Ricard (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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.

Keywords: Functional calculus; -spaces; Noncommutative Lp

Domains: Mathematics [math]; Functional Analysis [math.FA]

Éric Ricard. Fractional powers on noncommutative L p for p < 1. Advances in Mathematics, 2018, 333, pp.194-211. ⟨10.1016/j.aim.2018.05.024⟩. ⟨hal-01817762⟩