A nonlinear extension of the Birkhoff-Jentzsch theorem (Q1085420)
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scientific article; zbMATH DE number 3981898
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A nonlinear extension of the Birkhoff-Jentzsch theorem |
scientific article; zbMATH DE number 3981898 |
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A nonlinear extension of the Birkhoff-Jentzsch theorem (English)
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1986
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The theorem on positive matrices proved by Perron has been extended to certain positive linear operators in ordered vector spaces by Jentzsch and later by Birkhoff. In the present paper, the author gives a nonlinear version of the previous results for a class of operators which includes concave operators. For the proof it is required that the positive cone is complete with respect to the Hilbert's metric. Necessary and sufficient conditions in order for it to occur are given.
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positive linear operators in ordered vector spaces
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concave operators
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positive cone
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complete with respect to the Hilbert's metric
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