Fractional powers on noncommutative $L_p$ for $p<1$

Abstract

We prove that the homogeneous functional calculus associated to $x\mapsto |x{|}^{\theta }$ or $x\mapsto \mathrm{sgn}(x)|x{|}^{\theta }$ for $0<\theta <1$ is $\theta$-Hölder on selfadjoint elements of noncommutative $L_p$-spaces for $0<p\le \infty$ with values in $L_{p/\theta }$. This extends an inequality of Birman, Koplienko and Solomjak also obtained by Ando.

References in corpus (1)

• Functions of self-adjoint operators in ideals of compact operators