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Smooth derivations commuting with Lie group actions

Published online by Cambridge University Press:  24 October 2008

F. M. Goodman ,
P. E. T. Jorgensen  and
C. Peligrad
F. M. Goodman
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, IA 52242, U.S.A.
P. E. T. Jorgensen
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, IA 52242, U.S.A.
C. Peligrad
Affiliation:
Department of Mathematics, University of Cincinnati, Cincinnati, OH 45221, U.S.A.
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Extract

N. S. Poulsen, motivated in part by questions from relativistic quantum scattering theory, studied symmetric operators S in Hilbert space commuting with a unitary representation U of a Lie group G. (The group of interest in the physical setting is the Poincaré group.) He proved ([17], corollary 2·2) that if S is defined on the space of C∞-vectors for U (i.e. D(S) ⊇ ℋ∞(U)), then S is essentially self-adjoint.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 2 , March 1986 , pp. 307 - 314
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

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