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arXiv · 1107.5244

Completely positive multipliers of quantum groups

Matthew Daws
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Abstract

We show that any completely positive multiplier of the convolution algebra of the dual of an operator algebraic quantum group $\G$ (either a locally compact quantum group, or a quantum group coming from a modular or manageable multiplicative unitary) is induced in a canonical fashion by a unitary corepresentation of $\G$. It follows that there is an order bijection between the completely positive multipliers of $L^1(\G)$ and the positive functionals on the universal quantum group $C_0^u(\G)$. We provide a direct link between the Junge, Neufang, Ruan representation result and the representing element of a multiplier, and use this to show that their representation map is always weak$^*$-weak$^*$-continuous.

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Matthew Daws. 2011-07-26. Completely positive multipliers of quantum groups. https://doi.org/10.1142/s0129167x12501327

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