On spectral stability for self-adjoint extensions
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918395241299968 |
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| author | Caballero, Mario Alberto Ruiz |
| author_facet | Caballero, Mario Alberto Ruiz |
| contents | We prove that given a symmetric completely non-selfadjoint operator $B$ with finite deficiency indices $(n,n)$ on a Hilbert space and a boundary triplet $\left(\mathbb{C}^{n},Γ_{1},Γ_{2}\right)$ for $B^{*}$, the set of points in the spectrum of $A_{1}$ (the self-adjoint extension with domain $Ker\;Γ_{1}$) which are not eigenvalues of maximum multiplicity for any self-adjoint extension of $B$ disjoint of $A_{1}$, is a dense $\textit{G}_δ$ set in $σ(A_{1})$. Furthermore, a proof of a Malamud's theorem that generalizes a well-known result of the Aronszajn-Donoghue theory on the characterization of eigenvalues is offered. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17213 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On spectral stability for self-adjoint extensions Caballero, Mario Alberto Ruiz Spectral Theory 47B02, 47B25, 47A55, 47A10 We prove that given a symmetric completely non-selfadjoint operator $B$ with finite deficiency indices $(n,n)$ on a Hilbert space and a boundary triplet $\left(\mathbb{C}^{n},Γ_{1},Γ_{2}\right)$ for $B^{*}$, the set of points in the spectrum of $A_{1}$ (the self-adjoint extension with domain $Ker\;Γ_{1}$) which are not eigenvalues of maximum multiplicity for any self-adjoint extension of $B$ disjoint of $A_{1}$, is a dense $\textit{G}_δ$ set in $σ(A_{1})$. Furthermore, a proof of a Malamud's theorem that generalizes a well-known result of the Aronszajn-Donoghue theory on the characterization of eigenvalues is offered. |
| title | On spectral stability for self-adjoint extensions |
| topic | Spectral Theory 47B02, 47B25, 47A55, 47A10 |
| url | https://arxiv.org/abs/2603.17213 |