Complementable Operators and their Schur Complements

Published 17 Jun 2024 in math.FA | (2406.11457v1)

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.

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