English

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 CC^*-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

R2 v1 2026-06-28T08:35:53.322Z