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


Author: Mehrdad Kalantar
Journal: Proc. Amer. Math. Soc. 141 (2013), 3969-3976
MSC (2010): Primary 46L52, 46L53, 46L65
DOI: https://doi.org/10.1090/S0002-9939-2013-11763-6
Published electronically: July 29, 2013
MathSciNet review: 3091787
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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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Additional Information

Mehrdad Kalantar
Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
Email: mkalanta@math.carleton.ca

DOI: https://doi.org/10.1090/S0002-9939-2013-11763-6
Received by editor(s): January 29, 2012
Published electronically: July 29, 2013
Communicated by: Marius Junge
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.