PreprintCC BY 4.0arXiv
Spectral embedding through weak* limit of finite-dimensional approximations
Abstract
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 L2 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.
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BibTeX
@misc{nonez2026spectral,
title = {{Spectral embedding through weak* limit of finite-dimensional approximations}},
author = {Fabrice Nonez},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.30186},
eprint = {2605.30186},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.30186},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Spectral embedding through weak* limit of finite-dimensional approximations
AU - Fabrice Nonez
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2605.30186
UR - https://arxiv.org/abs/2605.30186
AB - 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.
ER -