On $C$-Symmetric and $C$-Self-adjoint Unbounded Operators on Hilbert Space
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912639035113472 |
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| author | Arlinskii, Yury Schmüdgen, Konrad |
| author_facet | Arlinskii, Yury Schmüdgen, Konrad |
| contents | Let $C$ be a conjugation on a Hilbert space $\mathcal{H}$. A densely defined linear operator $A$ on $\mathcal{H}$ is called $C$-symmetric if $CAC\subseteq A^*$ and $C$-self-adjoint if $CAC=A^*$. Our main results describe all $C$-self-adjoint extensions of $A$ on $\mathcal{H}$. Further, we prove a $C$-self-adjointness criterion based on quasi-analytic vectors and we characterize $C$-self-adjoint operators in terms of their polar decompositions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01847 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On $C$-Symmetric and $C$-Self-adjoint Unbounded Operators on Hilbert Space Arlinskii, Yury Schmüdgen, Konrad Functional Analysis 47B02 Let $C$ be a conjugation on a Hilbert space $\mathcal{H}$. A densely defined linear operator $A$ on $\mathcal{H}$ is called $C$-symmetric if $CAC\subseteq A^*$ and $C$-self-adjoint if $CAC=A^*$. Our main results describe all $C$-self-adjoint extensions of $A$ on $\mathcal{H}$. Further, we prove a $C$-self-adjointness criterion based on quasi-analytic vectors and we characterize $C$-self-adjoint operators in terms of their polar decompositions. |
| title | On $C$-Symmetric and $C$-Self-adjoint Unbounded Operators on Hilbert Space |
| topic | Functional Analysis 47B02 |
| url | https://arxiv.org/abs/2507.01847 |