# Completely isometric representations of $M_{cb}A(G)$ and $UCB(\hat G)^*$

@article{Neufang2008CompletelyIR, title={Completely isometric representations of \$M\_\{cb\}A(G)\$ and \$UCB(\hat G)^*\$}, author={Matthias Neufang and Zhong‐Jin Ruan and Nico Spronk}, journal={Transactions of the American Mathematical Society}, year={2008}, volume={360}, pages={1133-1162} }

. Let G be a locally compact group. It is shown that there exists a natural completely isometric representation of the completely bounded Fourier multiplier algebra M cb A ( G ), which is dual to the representation of the measure algebra M ( G ), on B ( L 2 ( G )). The image algebras of M ( G ) and M cb A ( G ) in CB σ ( B ( L 2 ( G ))) are intrinsically characterized, and some commutant theorems are proved. It is also shown that for any amenable group G , there is a natural completely…

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