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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Common eigenvectors for commutative positive linear operators

Author: Robert E. Huff
Journal: Proc. Amer. Math. Soc. 25 (1970), 51-55
MSC: Primary 47.20
MathSciNet review: 0257772
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Abstract: The purpose of this note is to point out an extension of the Markov-Kakutani fixed-point theorem to a result on the existence of a common eigenvector in a cone with a compact base when acted upon by a commutative family of operators. As an application, an extension is given of a result of Kreĭn and Rutman on characteristic functionals.

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Keywords: Common eigenvectors, fixed-points, locally convex spaces, ordered linear spaces, Markov-Kakutani Theorem, compact base, characteristic functional
Article copyright: © Copyright 1970 American Mathematical Society