Transference for Banach space representations of nilpotent Lie groups. Part 1. Irreducible representations
Representation Theory
2019-05-09 v3 Classical Analysis and ODEs
Functional Analysis
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.
Keywords
Cite
@article{arxiv.1511.08359,
title = {Transference for Banach space representations of nilpotent Lie groups. Part 1. Irreducible representations},
author = {Ingrid Beltita and Daniel Beltita and Jose E. Gale},
journal= {arXiv preprint arXiv:1511.08359},
year = {2019}
}
Comments
11 pages