Work

On non-negative operators in Krein spaces and their perturbations

Year: 2026

Type: article

Abstract: One of the most important contributions of Heinz Langer in the area of operator theory in Krein spaces is the introduction of the notion of definitizable operators and the construction of the corresponding spectral function. In this note we obtain a new characterization for the subclass of non-negative operators in Krein spaces which is based on local sign type properties of the spectrum and growth conditions on the resolvent. Based on these local properties, a notion of local non-negativity for self-adjoint operators in Krein spaces is defined and it is shown that such classes of operators appear naturally as perturbations of non-negative operators.

Source: Integral Equations and Operator Theory

DOI: 10.1007/s00020-026-02855-9

Authors: Jussi Behrndt, Friedrich M. Philipp, Carsten Trunk

Institutions: Graz University of Technology, Technische Universität Ilmenau

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,290

Funder: Deutsche Forschungsgemeinschaft