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

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

2012-03-12

arxiv.org/abs/1203.2594v1

Mathematics

Operator Algebras

Scientific paper

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

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