On harmonic non-commutative 𝐿^{𝑝}-operators on locally compact quantum groups

Kalantar, Mehrdad

doi:10.1090/S0002-9939-2013-11763-6

On harmonic non-commutative $L^p$-operators on locally compact quantum groups
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by Mehrdad Kalantar PDF

Proc. Amer. Math. Soc. 141 (2013), 3969-3976 Request permission

Abstract:

For a locally compact quantum group $\mathbb G$ with tracial Haar weight $\varphi$ and a quantum measure $\mu$ on $\mathbb G$, we study the space ${\mathcal {H}_\mu ^p(\mathbb G)}$ of $\mu$-harmonic operators in the non-commutative $L^p$-space ${\mathcal {L}^p(\mathbb G)}$ associated to the Haar weight $\varphi$. The main result states that if $\mu$ is non-degenerate, then ${\mathcal {H}_\mu ^p(\mathbb G)}$ is trivial for all $1\leq p<\infty$.

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