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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 ShargorodskyLet $H$ 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 $\cH$.
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Publication status
- Published
Journal
Journal of Operator TheoryISSN
1841-7744Publisher
Theta FoundationIssue
1Volume
44Page range
43-62ISBN
0379-4024Department affiliated with
- Mathematics Publications
Full text available
- No
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06Usage metrics
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