A Note on Spectral Convergence in Varying Hilbert Spaces

Frank Rösler

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arXiv · 1812.02525

A Note on Spectral Convergence in Varying Hilbert Spaces

Frank Rösler

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Abstract

We prove sufficient conditions for Hausdorff convergence of the spectra of sequences of closed operators defined on varying Hilbert spaces and converging in norm-resolvent sense, i.e. $\|J_\varepsilon(1+A_\varepsilon)^{-1} - (1+A)^{-1}J_\varepsilon\|\to 0$ as $\varepsilon\to 0$, where $J_\varepsilon$ is a suitable identification operator between the domains of the operators. This is an extension of results of [Mugnolo-Nittka-Post(2013)], who proved absence of spectral pollution for sectorial operators.

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BibTeX RIS

Frank Rösler. 2018-12-06. A Note on Spectral Convergence in Varying Hilbert Spaces. https://arxiv.org/abs/1812.02525

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