Common eigenvectors for commutative positive linear operators
HTML articles powered by AMS MathViewer
- by Robert E. Huff
- Proc. Amer. Math. Soc. 25 (1970), 51-55
- DOI: https://doi.org/10.1090/S0002-9939-1970-0257772-X
- PDF | Request permission
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
- L. N. Argabright, Invariant means and fixed points: A sequel to Mitchell’s paper, Trans. Amer. Math. Soc. 130 (1968), 127–130. MR 217578, DOI 10.1090/S0002-9947-1968-0217578-X
- Mahlon M. Day, Amenable semigroups, Illinois J. Math. 1 (1957), 509–544. MR 92128
- Mahlon M. Day, Fixed-point theorems for compact convex sets, Illinois J. Math. 5 (1961), 585–590. MR 138100
- Nelson Dunford and Jacob T. Schwartz, Linear Operators. I. General Theory, Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York; Interscience Publishers Ltd., London, 1958. With the assistance of W. G. Bade and R. G. Bartle. MR 0117523
- J. L. Kelley and Isaac Namioka, Linear topological spaces, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, Kennan T. Smith. MR 0166578
- M. G. Kreĭn and M. A. Rutman, Linear operators leaving invariant a cone in a Banach space, Uspehi Matem. Nauk (N.S.) 3 (1948), no. 1(23), 3–95 (Russian). MR 0027128
- Anthony L. Peressini, Ordered topological vector spaces, Harper & Row, Publishers, New York-London, 1967. MR 0227731
- R. J. Silverman and Ti Yen, Characteristic functionals, Proc. Amer. Math. Soc. 10 (1959), 471–477. MR 109301, DOI 10.1090/S0002-9939-1959-0109301-4
Bibliographic Information
- © Copyright 1970 American Mathematical Society
- 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