On large submodules in Hilbert C*-modules
Operator Algebras
2024-07-19 v2
Abstract
We consider several natural ways of expressing the idea that a one-sided ideal in a C*-algebra (or a submodule in a Hilbert C*-module) is large, and show that they differ, unlike the case of two-sided ideals in C*-algebras. We then show how these different notions, for ideals and for submodules, are related. We also study some permanence properties for these notions. Finally, we use essential right ideals to extend the inner product on a Hilbert C*-module to a part of the dual module.
Keywords
Cite
@article{arxiv.2402.07288,
title = {On large submodules in Hilbert C*-modules},
author = {V. Manuilov},
journal= {arXiv preprint arXiv:2402.07288},
year = {2024}
}
Comments
New title. Results of the previous version became a special case of the new ones. Replacement (instead of uploading new results separately) was done according to the recommendation of arxive moderators