Defines and studies the essential numerical range We(T) for unbounded Hilbert space operators, showing it captures spectral pollution in projection and truncation approximations.
Local convergence of spectra and pseudospectra
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abstract
We prove local convergence results for the spectra and pseudospectra of sequences of linear operators acting in different Hilbert spaces and converging in generalised strong resolvent sense to an operator with possibly non-empty essential spectrum. We establish local spectral exactness outside the limiting essential spectrum, local $\varepsilon$-pseudospectral exactness outside the limiting essential $\varepsilon$-near spectrum, and discuss properties of these two notions including perturbation results.
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math.SP 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
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The essential numerical range for unbounded linear operators
Defines and studies the essential numerical range We(T) for unbounded Hilbert space operators, showing it captures spectral pollution in projection and truncation approximations.