Locally definite normal operators in Krein spaces

2011/06/14 by Friedrich Philipp, Philipp, Friedrich
Computer Science · Mathematics · #47A11 #47A25 #47B50 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1106.2579

openalex publication_date 2011/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the spectral points of two-sided positive type of bounded normal operators in Krein spaces. It is shown that a normal operator has a local spectral function on sets which are of two-sided positive type. In addition, we prove that the Riesz-Dunford spectral subspace corresponding to a spectral set which is only of positive type is uniformly positive. The restriction of the operator to this subspace is then normal in a Hilbert space.

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