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Convergence theorems for intermediate problems

Published online by Cambridge University Press:  14 November 2011

Christopher A. Beattie  and
W. M. Greenlee
Christopher A. Beattie
Affiliation:
Department of Mathematics, University of Arizona, Tucson, Arizona 85721, U.S.A.
W. M. Greenlee
Affiliation:
Department of Mathematics, University of Arizona, Tucson, Arizona 85721, U.S.A.
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Synopsis

General convergence theorems are established for the lower part of the intermediate operator spectra arising in lower bound methods of Aronszajn type.Convergence of the T*T method is considered in detail, as are constructions that allow perturbations that are nonclosable in the underlying Hilbert space. Problems with essential spectra are admitted, as is the use of infinite rank projections capable of displacing essential spectra. These last features are necessary for a theory applicable to Schrodinger operators corresponding to atomic systems.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 100 , Issue 1-2 , 1985 , pp. 107 - 122
Copyright
Copyright © Royal Society of Edinburgh 1985

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