Transactions of the American Mathematical Society

Author(s): Matthias Neufang; Zhong-Jin Ruan; Nico Spronk
Journal: Trans. Amer. Math. Soc. 360 (2008), 1133-1161.
MSC (2000): Primary 22D15, 22D20, 43A10, 43A22, 46L07, 46L10, 47L10
Posted: October 16, 2007
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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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Matthias Neufang
Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
Email: mneufang@math.carleton.ca

Zhong-Jin Ruan
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Email: ruan@math.uiuc.edu

Nico Spronk
Affiliation: Department of Mathematics, University of Walterloo, Waterloo, Ontario, Canada N2L 3G1
Email: nspronk@math.uwaterloo.ca

DOI: 10.1090/S0002-9947-07-03940-2
PII: S 0002-9947(07)03940-2
Received by editor(s): October 26, 2004
Received by editor(s) in revised form: December 22, 2004
Posted: October 16, 2007
Additional Notes: The first and third authors were partially supported by NSERC
The second author was partially supported by the National Science Foundation DMS-0140067 and DMS-0500535
The third author was partially supported by an NSERC PDF
Copyright of article: Copyright 2007, American Mathematical Society

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