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arXiv · 2108.10757

A matrix formula for Schur complements of nonnegative selfadjoint linear relations

Maximiliano Contino·Alejandra Maestripieri·Stefania Marcantognini
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Abstract

If a nonnegative selfadjoint linear relation $A$ in a Hilbert space and a closed subspace $\mathcal{S}$ are assumed to satisfy that the domain of $A$ is invariant under the orthogonal projector onto $\mathcal{S},$ then $A$ admits a particular matrix representation with respect to the decomposition $\mathcal{S} \oplus \mathcal{S}^{\perp}$. This matrix representation of $A$ is used to give explicit formulae for the Schur complement of $A$ on $\mathcal{S}$ as well as the $\mathcal{S}-$compression of $A$.

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Maximiliano Contino, Alejandra Maestripieri, Stefania Marcantognini. 2021-08-24. A matrix formula for Schur complements of nonnegative selfadjoint linear relations. https://arxiv.org/abs/2108.10757

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