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Proceedings of the American Mathematical Society

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



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