On singular points in the essential spectrum
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866918159336865792 |
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| author | Plakhotnikov, Alexander |
| author_facet | Plakhotnikov, Alexander |
| contents | The paper investigates the existence of a limit in the operator norm for a family of operators $T_z(H)= F(H-z)^{-1}F^*$ for $z$ tending to the real axis. The conditions for the $H$ operator and the rigging operator $F$ are established, under which the limit exists. Special attention is paid to the separation of cases when the limit point belongs and does not belong to the point spectrum $H$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_11025 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On singular points in the essential spectrum Plakhotnikov, Alexander Functional Analysis 47A55, 47A10, 47A70, 47A40 The paper investigates the existence of a limit in the operator norm for a family of operators $T_z(H)= F(H-z)^{-1}F^*$ for $z$ tending to the real axis. The conditions for the $H$ operator and the rigging operator $F$ are established, under which the limit exists. Special attention is paid to the separation of cases when the limit point belongs and does not belong to the point spectrum $H$. |
| title | On singular points in the essential spectrum |
| topic | Functional Analysis 47A55, 47A10, 47A70, 47A40 |
| url | https://arxiv.org/abs/2510.11025 |