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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
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.


References [Enhancements On Off] (What's this?)

  • [1] L. N. Argabright, Invariant means and fixed points: A sequel to Mitchell's paper, Trans. Amer. Math. Soc. 130 (1968), 127-130. MR 36 #667. MR 0217578 (36:667)
  • [2] M. M. Day, Amenable semigroups, Illinois J. Math. 1 (1957), 509-544. MR 19, 1067. MR 0092128 (19:1067c)
  • [3] -, Fixed point theorems for compact convex sets, Illinois J. Math. 5 (1961), 585-590. MR 25 #1547. MR 0138100 (25:1547)
  • [4] N. Dunford and J. T. Schwartz, Linear operators. I: General theory, Pure and Appl. Math., vol. 7, Interscience, New York, 1958. MR 22 #8302. MR 0117523 (22:8302)
  • [5] J. L. Kelley, I. Namioka, et al, Linear topological spaces, The University Series in Higher Math., Van Nostrand, Princeton, N. J., 1963. MR 29 #3851. MR 0166578 (29:3851)
  • [6] M. G. Kreĭn and M. R. Rutman, Linear operators leaving invariant a cone in a Banach space, Uspehi Mat. Nauk 3 (1948), no. 1 (23), 3-95; English transl., Amer. Math. Soc. Transl. (1) 10 (1962), 199-325. MR 10, 256. MR 0027128 (10:256c)
  • [7] A. L. Peressini, Ordered topological vector spaces, Harper & Row, New York, 1967. MR 37 #3315. MR 0227731 (37:3315)
  • [8] R. J. Silverman and T. Yen, Characteristic functionals, Proc. Amer. Math. Soc. 10 (1959), 471-477. MR 22 #187. MR 0109301 (22:187)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0257772-X
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

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