Journal of Operator Theory
Volume 44, Issue 1, Summer 2000 pp. 43-62.
Geometry of higher order relative spectra and projection methodsAuthors: Eugene Shargorodsky
Author institution: School of Mathematical Sciences, University of Sussex, Falmer, East Sussex, BN1 9QH, UK
Summary: Let H be a densely defined linear operator acting on a Hilbert space \cH, let P be the orthogonal projection onto a closed linear subspace \cL and let n∈\bn. The n-th order spectrum Specn(H,\cL) of H relative to \cL is the set of z∈\bC such that the restriction to \cL of the operator P(H−zI)nP is not invertible within the subspace \cL. We study restrictions which may be placed on this set under given assumptions on Spec(H) and the behaviour of Specn(H,\cL) as \cL increases towards \cH.
Keywords: Higher order relative spectra, orthogonal projections, projection methods
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