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Transference for Banach space representations of nilpotent Lie groups. Part 1. Irreducible representations


Authors: Ingrid Beltiţă, Daniel Beltiţă and José E. Galé
Journal: Proc. Amer. Math. Soc. 146 (2018), 5065-5075
MSC (2010): Primary 17B30; Secondary 22E25, 22E27
DOI: https://doi.org/10.1090/proc/14206
Published electronically: September 4, 2018
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Abstract: We establish a general CCR (liminarity) property for uniformly bounded irreducible representations of nilpotent Lie groups on reflexive Banach spaces, extending the well-known property of unitary irreducible representations of these groups on Hilbert spaces. We also prove that this conclusion fails for many representations on non-reflexive Banach spaces. Our approach to these results blends the method of transference from abstract harmonic analysis and a systematic use of spaces of smooth vectors with respect to Lie group representations.


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Additional Information

Ingrid Beltiţă
Affiliation: Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, Bucharest, Romania
Email: Ingrid.Beltita@imar.ro

Daniel Beltiţă
Affiliation: Institute of Mathematics “Simion Stoilow” of the Romanian Academy, P.O. Box 1-764, Bucharest, Romania
Email: Daniel.Beltita@imar.ro

José E. Galé
Affiliation: Departamento de matemáticas and I.U.M.A., Universidad de Zaragoza, 50009 Zara- goza, Spain
Email: gale@unizar.es

DOI: https://doi.org/10.1090/proc/14206
Keywords: Reflexive Banach space, nilpotent Lie group, transference
Received by editor(s): March 10, 2018
Published electronically: September 4, 2018
Additional Notes: This research was partly supported by Project MTM2013-42105-P and Project MTM2016-77710-P, fondos FEDER, Spain.
The two first-named authors have also been supported by a Grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0131.
The third-named author has also been supported by Project E-64, D.G. Aragón, Spain.
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2018 American Mathematical Society

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