Journal of Operator Theory

Volume 69, Issue 1, Winter 2013 pp. 161-193.

The

$L^p$ -Fourier transform on locally compact quantum groups

Authors: Martijn Caspers
Author institution: IMAPP, Radboud Universiteit, Nijmegen, 6525 AJ, The Netherlands

Summary: Using interpolation properties of non-commutative

$L^p$ -spaces associated with an arbitrary von Neumann algebra, we define an

$L^p$ -Fourier transform

$1 \leqslant p \leqslant 2$ 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.

DOI: http://dx.doi.org/10.7900/jot.2010aug22.1949
Keywords: locally compact quantum groups, Fourier transform, interpolation spaces

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