Banach Journal of Mathematical Analysis

A generalized Schur complement for nonnegative operators on linear spaces

J. Friedrich, M. Günther, and L. Klotz

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Extending the corresponding notion for matrices or bounded linear operators on a Hilbert space, we define a generalized Schur complement for a nonnegative linear operator mapping a linear space into its dual, and we derive some of its properties.

Article information

Banach J. Math. Anal., Volume 12, Number 3 (2018), 617-633.

Received: 1 August 2017
Accepted: 15 November 2017
First available in Project Euclid: 19 April 2018

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Mathematical Reviews number (MathSciNet)

Primary: 47A05: General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
Secondary: 47A07: Forms (bilinear, sesquilinear, multilinear)

Schur complement square root shorted operator Albert’s theorem extremal operator


Friedrich, J.; Günther, M.; Klotz, L. A generalized Schur complement for nonnegative operators on linear spaces. Banach J. Math. Anal. 12 (2018), no. 3, 617--633. doi:10.1215/17358787-2017-0061.

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