A matrix formula for Schur complements of nonnegative selfadjoint linear relations

2021/08/24 by Maximiliano Contino, Contino, Maximiliano, Alejandra Maestripieri +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Quantum optics and atomic interactions

paper · pdf · doi:10.48550/arxiv.2108.10757

Abstract

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

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