Spectral embedding through weak* limit of finite-dimensional approximations
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866917544651128832 |
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| author | Nonez, Fabrice |
| author_facet | Nonez, Fabrice |
| contents | The scope of this text is to study a process that induces another proof of the Spectral Embedding Theorem: that any densely defined symmetric operator can be extended by a multiplication operator through an embedding of the Hilbert space into an $L_2$ space. Furthermore, that process is meant to be used for specific operators, where natural spectral embeddings or equivalences may be found.
That process has previously been considered in arXiv:2411.06281 and in arXiv:2511.18189, where it has been introduced through nonstandard techniques. Our contribution aims to be the reformulation of the theory through classical analysis arguments, without the use of nonstandard techniques nor ultraproducts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30186 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral embedding through weak* limit of finite-dimensional approximations Nonez, Fabrice Functional Analysis Logic Spectral Theory The scope of this text is to study a process that induces another proof of the Spectral Embedding Theorem: that any densely defined symmetric operator can be extended by a multiplication operator through an embedding of the Hilbert space into an $L_2$ space. Furthermore, that process is meant to be used for specific operators, where natural spectral embeddings or equivalences may be found. That process has previously been considered in arXiv:2411.06281 and in arXiv:2511.18189, where it has been introduced through nonstandard techniques. Our contribution aims to be the reformulation of the theory through classical analysis arguments, without the use of nonstandard techniques nor ultraproducts. |
| title | Spectral embedding through weak* limit of finite-dimensional approximations |
| topic | Functional Analysis Logic Spectral Theory |
| url | https://arxiv.org/abs/2605.30186 |