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Completely isometric representations of

Authors:	Matthias Neufang Zhong-Jin Ruan Nico Spronk

Institution:	School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6 ; Department of Mathematics, University of Illinois, Urbana, Illinois 61801 ; Department of Mathematics, University of Walterloo, Waterloo, Ontario, Canada N2L 3G1

Abstract:	Let 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 , on $\mathcal{B}(L_2(G))$ . The image algebras of and $M_{cb}A(G)$ in $\mathcal{CB}^{\sigma} (\mathcal{B}(L_2(G)))$ are intrinsically characterized, and some commutant theorems are proved. It is also shown that for any amenable group , there is a natural completely isometric representation of $UCB(\hat G)^*$ on $\mathcal{B}(L_2(G))$ , which can be regarded as a duality result of Neufang's completely isometric representation theorem for .

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