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

Beltiţă, Ingrid; Beltiţă, Daniel; Galé, José

doi:10.1090/proc/14206

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.

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