Self-adjoint extensions with compact resolvent
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866909992145125376 |
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| author | Wang, Yicao |
| author_facet | Wang, Yicao |
| contents | Let $T$ be a densely defined closed symmetric operator with equal deficiency indices in a separable complex Hilbert space $H$. In this paper, we prove that $T$ has a self-adjoint extension with compact resolvent if and only if the domain $D(T)$ of $T$ is compactly embedded in $H$ w.r.t. the graph norm on $D(T)$. If it is the case, we also prove that all self-adjoint extensions with compact resolvent can be parameterized by unitary operators $U$ on a certain Hilbert space such that $U-Id$ is compact. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_11074 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Self-adjoint extensions with compact resolvent Wang, Yicao Functional Analysis 47B25, 47A10 Let $T$ be a densely defined closed symmetric operator with equal deficiency indices in a separable complex Hilbert space $H$. In this paper, we prove that $T$ has a self-adjoint extension with compact resolvent if and only if the domain $D(T)$ of $T$ is compactly embedded in $H$ w.r.t. the graph norm on $D(T)$. If it is the case, we also prove that all self-adjoint extensions with compact resolvent can be parameterized by unitary operators $U$ on a certain Hilbert space such that $U-Id$ is compact. |
| title | Self-adjoint extensions with compact resolvent |
| topic | Functional Analysis 47B25, 47A10 |
| url | https://arxiv.org/abs/2601.11074 |