# A REPRESENTATION THEOREM FOR LOCALLY COMPACT QUANTUM GROUPS

@article{Junge2009ART, title={A REPRESENTATION THEOREM FOR LOCALLY COMPACT QUANTUM GROUPS}, author={Marius Junge and Matthias Neufang and Zhong‐Jin Ruan}, journal={International Journal of Mathematics}, year={2009}, volume={20}, pages={377-400} }

Recently, Neufang, Ruan and Spronk proved a completely isometric representation theorem for the measure algebra M(G) and for the completely bounded (Herz–Schur) multiplier algebra McbA(G) on $\mathcal{B}(L_{2}(G))$, where G is a locally compact group. We unify and generalize both results by extending the representation to arbitrary locally compact quantum groups 𝔾 = (M, Γ, φ, ψ). More precisely, we introduce the algebra $M_{\rm cb}^{r} (L_1(\mathbb{G}))$ of completely bounded right multipliers…

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