Hölder estimates for the noncommutative Mazur maps

Abstract

For any von Neumann algebra $\mathcal{M}$, the noncommutative Mazur map $M_{p,q}$ from $L_p(\mathcal{M})$ to $L_q(\mathcal{M})$ with $1\le p,q<\infty$ is defined by $f\mapsto f|f{|}^{\frac{p-q}{q}}$. In analogy with the commutative case, we gather estimates showing that $M_{p,q}$ is $\min \{\frac{p}{q},1\}$-Hölder on balls.

Better estimates on the constants, removes a mistake

Cited by in corpus (2)

• Fixed-point spectrum for group actions by affine isometries on Lp-spaces
• Local rigidity for actions of Kazhdan groups on non commutative $L_p$-spaces