On Harmonic Noncommutative $L^p$-Operators on Locally Compact Quantum Groups

Mehrdad Kalantar

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arXiv · 1203.2594

On Harmonic Noncommutative $L^p$-Operators on Locally Compact Quantum Groups

Mehrdad Kalantar

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Abstract

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

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Mehrdad Kalantar. 2012-03-12. On Harmonic Noncommutative $L^p$-Operators on Locally Compact Quantum Groups. https://arxiv.org/abs/1203.2594

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