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 Lp/θ. This extends an inequality of Birman, Koplienko and Solomjak also obtained by Ando.

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