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arXiv · 2110.09708

Operator $\theta$-H\"{o}lder functions with respect to $\left\|\cdot\right\|_p$, $0< p\le \infty$

Jinghao Huang·Fedor Sukochev·Dmitriy Zanin
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Abstract

Let $\theta \in(0,1)$ and $(\mathcal{M},\tau)$ be a semifinite von Neumann algebra. We consider the function spaces introduced by Sobolev (denoted by $S_{d,\theta}$), showing that there exists a constant $d>0 $ depending on $p$, $0 1$, we obtain a reverse of the Birman-Koplienko-Solomjak inequality, which extends a couple of existing results on fractional powers $t\mapsto t^\theta$ by Ando et al.

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Jinghao Huang, Fedor Sukochev, Dmitriy Zanin. 2021-10-19. Operator $\theta$-H\"{o}lder functions with respect to $\left\|\cdot\right\|_p$, $0< p\le \infty$. https://arxiv.org/abs/2110.09708

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