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

Details The L^p-Fourier transform on locally compact quantum groups The L^p-Fourier transform on locally compact quantum groups

2010-08-16

arxiv.org/abs/1008.2603v2

Mathematics

Operator Algebras

29 pages, to appear in the Journal of Operator Theory

Scientific paper

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.

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