Locus of non-real eigenvalues of a class of linear relations in a Krein space

2024/10/22 by Rytis Juršėnas, Jursenas, Rytis
Mathematics · #advanced mathematical theories #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2410.16725

Abstract

It is a classical result that, if a maximal symmetric operator T in a Krein space H=H^-[⊕]H⁺ has the property H^-\subseteqD_T, then the imaginary part of its eigenvalue λ from upper or lower half-plane is bounded by | Im λ|≤2‖ TP^- ‖. We prove that in both half-planes | Im λ| never exceeds t₀‖ TP^- ‖ for some constant t₀≈1.84. The result applies to a closed symmetric relation T and carries on a suitable, most notably dissipative, extension.

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