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

2011/12/09 by Behrndt, Jussi, Leben, Leslie, Philipp, Friedrich
#47A11 #47A55 #47B50 #FOS: Mathematics #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1112.2096

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 ℓ^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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