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Geometry of higher order relative spectra and projection methods

journal contribution
posted on 2023-06-07, 23:40 authored by Eugene Shargorodsky
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 $\cH$.

History

Publication status

  • Published

Journal

Journal of Operator Theory

ISSN

1841-7744

Publisher

Theta Foundation

Issue

1

Volume

44

Page range

43-62

ISBN

0379-4024

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

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