The L^p-Fourier transform on locally compact quantum groups
Operator Algebras
2011-07-26 v2 Quantum Algebra
Abstract
Using interpolation properties of non-commutative L^p-spaces associated with an arbitrary von Neumann algebra, we define a L^p-Fourier transform 1 <= p <= 2 on locally compact quantum groups. We show that the Fourier transform determines a distinguished choice for the interpolation parameter as introduced by Izumi. We define a convolution product in the L^p-setting and show that the Fourier transform turns the convolution product into a product.
Cite
@article{arxiv.1008.2603,
title = {The L^p-Fourier transform on locally compact quantum groups},
author = {Martijn Caspers},
journal= {arXiv preprint arXiv:1008.2603},
year = {2011}
}
Comments
29 pages, to appear in the Journal of Operator Theory