Journal article
Point-spectrum of semibounded operator extensions
Proceedings of the American Mathematical Society, Vol.81(4), pp.565-569
04/01/1981
DOI: 10.1090/S0002-9939-1981-0601731-9
Abstract
Let H denote the Friedrichs extension of a given semibounded operator H in a Hilbert space. Assume λI < H, and λ € σ(H). If for a finite-dimensional projection P in the Hilbert space we have I— P < Const.(H — λI), then it follows that A is an eigenvalue of H, and the corresponding eigenspace is contained in the range of P. Using this, together with the known order structure on the family of selfadjoint extensions, with given lower bound 0, of minus the Laplace-Beltrami operator, we establish the identity (Ug(l) = 1 for all g E G for the following problem. U is a unitary representation of a Lie group G, and acts on the Hilbert space L2(iI) for some Nikodym-domain flcG. Moreover U is obtained as a certain normalized integral for the left-G-invariant vector fields on Q, that is, for each such vector field X, the skew-adjoint operator dU(X) is an extension of X when regarded as a skew-symmetric operator in L2(Q) with domain Co°(Q).
Details
- Title: Subtitle
- Point-spectrum of semibounded operator extensions
- Creators
- Palle E.T. J0rgensen - University of Iowa, Mathematics
- Resource Type
- Journal article
- Publication Details
- Proceedings of the American Mathematical Society, Vol.81(4), pp.565-569
- DOI
- 10.1090/S0002-9939-1981-0601731-9
- ISSN
- 0002-9939
- eISSN
- 1088-6826
- Publisher
- American Mathematical Society
- Number of pages
- 5
- Language
- English
- Date published
- 04/01/1981
- Academic Unit
- Mathematics
- Record Identifier
- 9983985888702771
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