Complementable Operators and their Schur Complements
Sachin Manjunath Naik, P. Sam Johnson
TL;DR
This paper characterizes complementable operators, provides explicit formulas for their Schur complements using Douglas solutions, and explores their range-Hermitian properties, advancing understanding of operator complementability.
Contribution
It introduces a new characterization of complementable operators and derives explicit Schur complement formulas using Douglas solutions.
Findings
Explicit Schur complement expressions for complementable operators
Existence of subspaces where operators are invariably complementable
Analysis of the range-Hermitian property of these operators
Abstract
In this paper, we characterize complementable operators and provide more precise expressions for the Schur complement of these operators using a single Douglas solution. We demonstrate the existence of subspaces where the given operator is invariably complementable. Additionally, we investigate the range-Hermitian property of these operators.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMatrix Theory and Algorithms · Holomorphic and Operator Theory · Advanced Topics in Algebra