On J-Self-Adjoint Operators with Stable C-Symmetry

TL;DR

This paper develops the theory of J-self-adjoint operators with stable C-symmetry in Krein spaces, focusing on extensions of symmetric operators with specific defect numbers, advancing understanding of their spectral properties.

Contribution

It introduces the concept of stable C-symmetry for J-self-adjoint extensions and analyzes its implications for operators with defect numbers less than 2,2.

Findings

Characterization of J-self-adjoint operators with stable C-symmetry

Detailed analysis for operators with defect numbers <2,2>

Extension of existing theory to new classes of operators

Abstract

The paper is devoted to a development of the theory of self-adjoint operators in Krein spaces (J-self-adjoint operators) involving some additional properties arising from the existence of C-symmetries. The main attention is paid to the recent notion of stable C-symmetry for J-self-adjoint extensions of a symmetric operator S. The general results are specialized further by studying in detail the case where S has defect numbers <2,2>.