Abstract
Let be a continuous unitary representation of the (infinite-dimen- sional) Lie group , and let be a group homomorphism which defines a continuous action of on by Lie group automorphisms. Let be a continuous unitary representation of the semidirect product group on . The first main theorem of the present note provides criteria for the invariance of the space of smooth vectors of under the operators for and , respectively. When is complete and the actions of on and are continuous, we use the above theorem to show that, for suitably defined spectral subspaces , , in the complexified Lie algebra and , , for in , we have
Citation
Karl-Hermann Neeb. Hadi Salmasian. Christoph Zellner. "On an invariance property of the space of smooth vectors." Kyoto J. Math. 55 (3) 501 - 515, September 2015. https://doi.org/10.1215/21562261-3089019
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