# Geometry of higher order relative spectra and projection methods

Shargorodsky, Eugene (2000) Geometry of higher order relative spectra and projection methods. Journal of Operator Theory, 44 (1). pp. 43-62. ISSN 1841-7744

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## Abstract

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 $n \in \bn$. The $n$-th order spectrum ${\rm Spec}_n(H,\cL)$ of $H$ relative to $\cL$ is the set of $z\in\bC$ 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 ${\rm Spec}(H)$ and the behaviour of ${\rm Spec}_n(H,\cL)$ as $\cL$ increases towards $\cH$.

Item Type: Article School of Mathematical and Physical Sciences > Mathematics EPrints Services 06 Feb 2012 19:40 09 Jul 2012 14:53 http://sro.sussex.ac.uk/id/eprint/21709