When is the sum of closed subspaces of a Hilbert space closed?

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).

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Bibliographic Details
Published in:arXiv.org 2020-12
Main Author: Feshchenko, Ivan
Format: Article
Language:English
Subjects:
Hilbert space
Subspaces
Online Access:Get full text
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Description
Summary: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).
ISSN:2331-8422