A Nonsmooth Continuous Unitary Representation of a Banach-Lie Group

被引：0
|
作者：
Beltita, Daniel [1 ]
Neeb, Karl-Hermann [2 ]
机构：
[1] Simion Stoilow Romanian Acad, Inst Math, Bucharest, Romania
[2] Tech Univ Darmstadt, Dept Math, D-64289 Darmstadt, Germany
来源：
JOURNAL OF LIE THEORY | 2008年 / 18卷 / 04期
关键词：
Infinite-dimensional Lie group; unitary representation; smooth vector;
D O I：
暂无
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this note we show that the representation of the additive group of the Hilbert space L(2)([0, 1], R) on L(2)([0, 1], C) given by the multiplication operators pi(f) := e(if) is continuous but its space of smooth vectors is trivial. This example shows that a continuous unitary representation of an infinite dimensional Lie group need not be smooth.
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页码：933 / 936
页数：4
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