Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

Convergence theorems for intermediate problems

Christopher A. Beattiea1 and W. M. Greenleea1

a1 Department of Mathematics, University of Arizona, Tucson, Arizona 85721, U.S.A.

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.

(Received September 23 1983)

(Accepted October 16 1984)