English

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).

Keywords

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