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Completely bounded $ \Lambda_p$ sets that are not Sidon


Authors: Kathryn Hare and Parasar Mohanty
Journal: Proc. Amer. Math. Soc. 144 (2016), 2861-2869
MSC (2010): Primary 43A46; Secondary 46L07, 47L25
DOI: https://doi.org/10.1090/proc/13039
Published electronically: March 18, 2016
MathSciNet review: 3487220
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Abstract: In this paper we construct examples of completely bounded $ \Lambda _p$ sets, which are not Sidon, on any compact abelian group. As a consequence, we have a new proof of the classical result for the existence of non-Sidon, $ \Lambda _p$ sets on any compact abelian group.


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Additional Information

Kathryn Hare
Affiliation: Department of Pure Mathematics, University of Waterloo, Ontario, Canada N2L 3G1
Email: kehare@uwaterloo.ca

Parasar Mohanty
Affiliation: Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, India, 208016
Email: parasar@iitk.ac.in

DOI: https://doi.org/10.1090/proc/13039
Keywords: Lacunary sets, completely bounded multipliers, non-commutative $\Lambda_p$ sets, Sidon sets
Received by editor(s): March 4, 2013
Received by editor(s) in revised form: February 4, 2014
Published electronically: March 18, 2016
Additional Notes: The first author was supported in part by NSERC grant number 45597.
The second author would like to thank the University of Waterloo for their hospitality.
Communicated by: Alexander Iosevich
Article copyright: © Copyright 2016 American Mathematical Society