Semiclosed projections and applications

TL;DR

This paper characterizes semiclosed projections and demonstrates their application in computing the Schur complement of selfadjoint operators, especially in contexts involving weak complementability.

Contribution

It introduces a characterization of semiclosed projections and applies them to Schur complement computation in operator theory.

Findings

Semiclosed projections are characterized mathematically.

Application to Schur complement computation for selfadjoint operators.

Relevance to weak complementability in operator theory.

Abstract

We characterize the semiclosed projections and apply them to compute the Schur complement of a selfadjoint operator with respect to a closed subspace. These projections occur naturally when dealing with weak complementability.