The intersection of complemented submodules is not complemented
Operator Algebras
2023-02-10 v1 Functional Analysis
Abstract
We show by (counter)example that the intersection of complemented submodules in a Hilbert -module is not necessarily complemented, answering an open question from [MR].
Keywords
Cite
@article{arxiv.2302.04631,
title = {The intersection of complemented submodules is not complemented},
author = {Koen van den Dungen and Bram Mesland and Adam Rennie},
journal= {arXiv preprint arXiv:2302.04631},
year = {2023}
}
Comments
Addendum to : The Friedrichs angle and alternating projections in Hilbert $C^*$-modules, J. Math. Anal. Appl. 516 (1) (2022) 126474, arXiv:2112.03822