Variation of discrete spectra of non-negative operators in Krein spaces

Jussi Behrndt; Leslie Leben; Friedrich Philipp

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arXiv · 1112.2096

Variation of discrete spectra of non-negative operators in Krein spaces

Jussi Behrndt·Leslie Leben·Friedrich Philipp

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Abstract

We study the variation of the discrete spectrum of a bounded non-negative operator in a Krein space under a non-negative Schatten class perturbation of order $p$. It turns out that there exist so-called extended enumerations of discrete eigenvalues of the unperturbed and the perturbed operator, respectively, whose difference is an $\ell^p$-sequence. This result is a Krein space version of a theorem by T.Kato for bounded selfadjoint operators in Hilbert spaces.

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BibTeX RIS

Jussi Behrndt, Leslie Leben, Friedrich Philipp. 2011-12-09. Variation of discrete spectra of non-negative operators in Krein spaces. https://arxiv.org/abs/1112.2096

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