The minus order and range additivity

The minus order and range additivity

We study the minus order on the algebra of bounded linear operators on a Hilbert space. By giving a characterization in terms of range additivity, we show that the intrinsic nature of the minus order is algebraic. Applications to generalized inverses of the sum of two operators, to systems of operat...

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Veröffentlicht in:Linear algebra and its applications 2017-10, Vol.531, p.234-256
Hauptverfasser: Djikić, Marko S., Fongi, Guillermina, Maestripieri, Alejandra
Format: Artikel
Sprache:eng
Schlagworte:
Addition & subtraction
Generalized inverses
Generalized linear models
Hilbert space
Least squares problems
Linear algebra
Linear operators
Mathematical problems
Minus order
Operators (mathematics)
Optimization
Range additivity
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Beschreibung
Zusammenfassung:We study the minus order on the algebra of bounded linear operators on a Hilbert space. By giving a characterization in terms of range additivity, we show that the intrinsic nature of the minus order is algebraic. Applications to generalized inverses of the sum of two operators, to systems of operator equations and to optimization problems are also presented.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2017.05.045