Transference for Banach space representations of nilpotent Lie groups. Part 1. Irreducible representations
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- by Ingrid Beltiţă, Daniel Beltiţă and José E. Galé PDF
- Proc. Amer. Math. Soc. 146 (2018), 5065-5075 Request permission
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.References
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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
- MR Author ID: 656639
- 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
- 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
- © Copyright 2018 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 146 (2018), 5065-5075
- MSC (2010): Primary 17B30; Secondary 22E25, 22E27
- DOI: https://doi.org/10.1090/proc/14206
- MathSciNet review: 3866846