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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1524124812

Digital Object Identifier
doi:10.1215/17358787-2017-0061

Mathematical Reviews number (MathSciNet)
MR3824743

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

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

Citation

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. https://projecteuclid.org/euclid.bjma/1524124812


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