$L_p$-Multipliers on Quantum Tori

Abstract

It was shown by Chen, Xu and Yin that completely bounded Fourier multipliers on noncommutative $L_p$-spaces of quantum tori ${\mathbb{T}}_{\theta }^d$ do not depend on the parameter $\theta$. We establish that the situation is somehow different for bounded multipliers. The arguments are based on transference from the commutative torus.

References in corpus (1)

• Noncommutative vector valued $L_p$-spaces and completely $p$-summing maps