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The L^p-Fourier transform on locally compact quantum groups
September 27th - October 1st, 2010, Conference on Quantum groups, free probability and non-commutative geometry (CIRM Luminy).
Abstract
We show how interpolation properties of von Neumann algebras can be applied to define a Fourier transform and
convolution product in the L^p-setting on locally compact quantum groups. The other way around, the L^p-Fourier transform reveals information about how
to interpolate between the predual of a von Neumann algebra and the von Neumann algebra itself. We specialize the theory in case the von Neumann
algebra of the (dual) quantum group is semi-finite or, moreover, type I.
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