TRANSFERENCE FOR BANACH SPACE REPRESENTATIONS OF NILPOTENT LIE GROUPS. PART 1. IRREDUCIBLE REPRESENTATIONS

被引：1

作者：

Beltita, Ingrid ^{[1
]}

Beltita, Daniel ^{[1
]}

Gale, Jose E. ^{[2
,3
]}

机构：

[1] Romanian Acad, Inst Math Simion Stoilow, POB 1-764, Bucharest, Romania

[2] Univ Zaragoza, Dept Matemat, E-50009 Zaragoza, Spain

[3] Univ Zaragoza, IUMA, E-50009 Zaragoza, Spain

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2018年 / 146卷 / 12期

关键词：

Reflexive Banach space; nilpotent Lie group; transference;

D O I：

10.1090/proc/14206

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：5065 / 5075

页数：11

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