Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

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


Authors: Matthias Neufang, Zhong-Jin Ruan and Nico Spronk
Journal: Trans. Amer. Math. Soc. 360 (2008), 1133-1161
MSC (2000): Primary 22D15, 22D20, 43A10, 43A22, 46L07, 46L10, 47L10
DOI: https://doi.org/10.1090/S0002-9947-07-03940-2
Published electronically: October 16, 2007
MathSciNet review: 2357691
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: 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 $\mathcal {B}(L_2(G))$. The image algebras of $M(G)$ 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 $G$, 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 $LUC(G)^*$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 22D15, 22D20, 43A10, 43A22, 46L07, 46L10, 47L10

Retrieve articles in all journals with MSC (2000): 22D15, 22D20, 43A10, 43A22, 46L07, 46L10, 47L10


Additional Information

Matthias Neufang
Affiliation: School of Mathematics and Statistics, Carleton University, Ottawa, Ontario, Canada K1S 5B6
MR Author ID: 718390
Email: mneufang@math.carleton.ca

Zhong-Jin Ruan
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
MR Author ID: 249360
Email: ruan@math.uiuc.edu

Nico Spronk
Affiliation: Department of Mathematics, University of Walterloo, Waterloo, Ontario, Canada N2L 3G1
MR Author ID: 671665
Email: nspronk@math.uwaterloo.ca

Received by editor(s): October 26, 2004
Received by editor(s) in revised form: December 22, 2004
Published electronically: 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
Article copyright: © Copyright 2007 American Mathematical Society