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arXiv · 2607.05852

Hermitian Pencils and their Representation in Krein Spaces

Rabeb Aydi·Omaima Kchaou·Carsten Trunk
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Abstract

Pencils of the form $\mathcal{A}({\lambda}) = {\lambda}E-A$ are studied, where $A$ and $E$ are bounded linear operators on a Hilbert space. Of interest are the spectral properties of $\mathcal{A}({\lambda})$. This is done via a corresponding linear relation in a Krein space, which is given in range representation using the two operators $A$ and $E$. Under some assumptions on $E$ and $A$, the linear relation in range representation is nonnegative or has finitely many negative squares. Then one uses spectral properties of linear relations and deduces spectral properties of the operator pencil $\mathcal{A}({\lambda}) = {\lambda}E-A$.

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Rabeb Aydi, Omaima Kchaou, Carsten Trunk. 2026-07-07. Hermitian Pencils and their Representation in Krein Spaces. https://arxiv.org/abs/2607.05852

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