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Extending multipliers of the Fourier algebra from a subgroup


Authors: Michael Brannan and Brian Forrest
Journal: Proc. Amer. Math. Soc. 142 (2014), 1181-1191
MSC (2000): Primary 43A30, 43A22; Secondary 46L07, 22D25, 22D10
DOI: https://doi.org/10.1090/S0002-9939-2014-11824-7
Published electronically: January 16, 2014
MathSciNet review: 3162241
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Abstract: In this paper, we consider various extension problems associated with elements in the closure with respect to either the multiplier norm or the completely bounded multiplier norm of the Fourier algebra of a locally compact group. In particular, we show that it is not always possible to extend an element in the closure with respect to the multiplier norm of the Fourier algebra of the free group on two generators to a multiplier of the Fourier algebra of $ SL(2,\mathbb{R})$.


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Additional Information

Michael Brannan
Affiliation: Department of Mathematics and Statistics, Queen’s University, 99 University Avenue, Kingston, ON, Canada, K7L 3N6
Email: mbrannan@mast.queensu.ca

Brian Forrest
Affiliation: Department of Pure Mathematics, University of Waterloo, Waterloo, ON, Canada, N2L 3G1
Email: beforrest@uwaterloo.ca

DOI: https://doi.org/10.1090/S0002-9939-2014-11824-7
Keywords: Fourier algebra, multipliers, completely bounded multipliers, locally compact group
Received by editor(s): April 13, 2011
Received by editor(s) in revised form: April 1, 2012
Published electronically: January 16, 2014
Communicated by: Marius Junge
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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