Common eigenvectors for commutative positive linear operators
Author:
Robert E. Huff
Journal:
Proc. Amer. Math. Soc. 25 (1970), 51-55
MSC:
Primary 47.20
DOI:
https://doi.org/10.1090/S0002-9939-1970-0257772-X
MathSciNet review:
0257772
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Abstract | References | Similar Articles | Additional Information
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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Additional Information
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