Spectral Theory for Non-full Commutative C*-categories
Abstract
We extend the spectral theory of commutative C*-categories to the non full-case, introducing a suitable notion of spectral spaceoid provinding a duality between a category of "non-trivial" *-functors of non-full commutative C*-categories and a category of Takahashi morphisms of "non-full spaceoids" (here defined). As a byproduct we obtain a spectral theorem for a non-full generalization of imprimitivity Hilbert C*-bimodules over commutative unital C*-algebras via continuous sections vanishing at infinity of a Hilbert C*-line-bundle over the graph of a homeomorphism between open subsets of the corresponding Gel'fand spectra of the C*-algebras.
Keywords
Cite
@article{arxiv.2502.00995,
title = {Spectral Theory for Non-full Commutative C*-categories},
author = {Paolo Bertozzini and Roberto Conti and Wicharn Lewkeeratiyutkul and Kasemsun Rutamorn},
journal= {arXiv preprint arXiv:2502.00995},
year = {2025}
}
Comments
AMS-LaTeX-2e, 34 pages, extended introduction unchanged, additional typos corrected, no significant change in the main text and in the results, reformatted arXiv version of the published paper