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The Extreme Points of Order Intervals of Positive Operators

✍ Scribed by W.L. Green; T.D. Morley

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 433 KB
Volume: 15
Category: Article
ISSN: 0196-8858
DOI: 10.1006/aama.1994.1013

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✦ Synopsis

Consider the order interval of operators ([0, A}={X \mid 0 \leq X \leq A}). In finite dimensions (or if (A) is invertible) then the extreme points of ([0, A]) are the shorted operators (generalized Schur complements) of (A). This is false in the general infinite dimensional case. We give an example arising from the discretization of the biharmonic equation. We also give necessary and sufficient conditions for an extreme point (X_{0}) to be a short of (A, 1994) Academic Press, Inc.

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