On the closedness of the sum of n subspaces of a Hilbert space
Ivan Feshchenko
TL;DR
This paper establishes necessary and sufficient conditions for the sum of multiple subspaces in a Hilbert space to be closed, and explores properties of such subspace configurations.
Contribution
It provides a complete characterization of when the sum of n subspaces is closed, advancing understanding of subspace sums in Hilbert spaces.
Findings
Characterization of closed sums of n subspaces
Properties of n-tuples of subspaces with closed sum
Conditions for sum closure in Hilbert spaces
Abstract
We give necessary and sufficient conditions for the sum of n subspaces of a Hilbert space to be closed. We also present various properties of n-tuples of subspaces with closed sum.
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Taxonomy
TopicsOptimization and Variational Analysis · Advanced Banach Space Theory · Advanced Optimization Algorithms Research