Locus of non-real eigenvalues of a class of linear relations in a Krein space
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916448760233984 |
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| author | Jursenas, Rytis |
| author_facet | Jursenas, Rytis |
| contents | It is a classical result that, if a maximal symmetric operator $T$ in a Krein space $\mathcal{H}=\mathcal{H}^-[\oplus]\mathcal{H}^+$ has the property $\mathcal{H}^-\subseteq\mathcal{D}_T$, then the imaginary part of its eigenvalue $λ$ from upper or lower half-plane is bounded by $\lvert \mathrm{Im}\,λ\rvert\leq2\lVert TP^- \rVert$. We prove that in both half-planes $\lvert \mathrm{Im}\,λ\rvert$ never exceeds $t_0\lVert TP^- \rVert$ for some constant $t_0\approx1.84$. The result applies to a closed symmetric relation $T$ and carries on a suitable, most notably dissipative, extension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16725 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Locus of non-real eigenvalues of a class of linear relations in a Krein space Jursenas, Rytis Spectral Theory Functional Analysis 47A06, 47B50, 47B25, 46C20 It is a classical result that, if a maximal symmetric operator $T$ in a Krein space $\mathcal{H}=\mathcal{H}^-[\oplus]\mathcal{H}^+$ has the property $\mathcal{H}^-\subseteq\mathcal{D}_T$, then the imaginary part of its eigenvalue $λ$ from upper or lower half-plane is bounded by $\lvert \mathrm{Im}\,λ\rvert\leq2\lVert TP^- \rVert$. We prove that in both half-planes $\lvert \mathrm{Im}\,λ\rvert$ never exceeds $t_0\lVert TP^- \rVert$ for some constant $t_0\approx1.84$. The result applies to a closed symmetric relation $T$ and carries on a suitable, most notably dissipative, extension. |
| title | Locus of non-real eigenvalues of a class of linear relations in a Krein space |
| topic | Spectral Theory Functional Analysis 47A06, 47B50, 47B25, 46C20 |
| url | https://arxiv.org/abs/2410.16725 |