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Spectral theorem for compact self-adjoint operators on smooth Banach spaces
Abstract
We establish a spectral representation theorem for compact operators that are self-adjoint with respect to the duality mapping on smooth Banach spaces. The result is a natural analogue of the classical spectral theorem for compact self-adjoint operators on Hilbert spaces.
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BibTeX
@misc{shameem2026spectral,
title = {{Spectral theorem for compact self-adjoint operators on smooth Banach spaces}},
author = {Mohammed Shameem},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.06873},
eprint = {2608.06873},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.06873},
}
RIS
TY - UNPB
TI - Spectral theorem for compact self-adjoint operators on smooth Banach spaces
AU - Mohammed Shameem
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2608.06873
UR - https://arxiv.org/abs/2608.06873
AB - We establish a spectral representation theorem for compact operators that are self-adjoint with respect to the duality mapping on smooth Banach spaces. The result is a natural analogue of the classical spectral theorem for compact self-adjoint operators on Hilbert spaces.
ER -