A non-smooth continuous unitary representation of a Banach-Lie group

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dc.creatorBeltita, Daniel
dc.creatorNeeb, Karl-Hermann
dc.date2008-11-26
dc.date.accessioned2026-07-07T12:04:28Z
dc.date.available2026-07-07T12:04:28Z
dc.descriptionIn 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 $π(f) := e^{if}$ 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.
dc.description5 pages
dc.identifierhttps://arxiv.org/abs/0811.4234
dc.identifierhttp://arxiv.org/abs/0811.4234
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/208142
dc.subjectRepresentation Theory
dc.subjectFunctional Analysis
dc.subject22E65; 22E45
dc.titleA non-smooth continuous unitary representation of a Banach-Lie group
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