When is the sum of closed subspaces of a Hilbert space closed?
Functional Analysis
2020-12-17 v1
Abstract
We provide a sufficient condition for a finite number of closed subspaces of a Hilbert space to be linearly independent and their sum to be closed. Under this condition a formula for the orthogonal projection onto the sum is given. We also show that this condition is sharp (in a certain sense).
Cite
@article{arxiv.2012.08688,
title = {When is the sum of closed subspaces of a Hilbert space closed?},
author = {Ivan Feshchenko},
journal= {arXiv preprint arXiv:2012.08688},
year = {2020}
}
Comments
arXiv admin note: text overlap with arXiv:1606.08048