Asymptotic convergence theorems for nonnegative operators on Banach lattices, on , on C(X) and on are proved. The general results are applied to a class of integral operators on L¹.
@article{bwmeta1.element.bwnjournal-article-apmv68z1p1bwm, author = {Jolanta Soca\l a}, title = {Asymptotic behaviour of the iterates of nonnegative operators on a Banach lattice}, journal = {Annales Polonici Mathematici}, volume = {69}, year = {1998}, pages = {1-16}, zbl = {0911.47031}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv68z1p1bwm} }
Jolanta Socała. Asymptotic behaviour of the iterates of nonnegative operators on a Banach lattice. Annales Polonici Mathematici, Tome 69 (1998) pp. 1-16. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv68z1p1bwm/
[000] [A] H. Amann, Fixed point theorems and nonlinear eigenvalue problems, SIAM Rev. 18 (1976), 620-709.
[001] [DS] N. Dunford and J. T. Schwartz, Linear Operators, Interscience Publ., New York, 1958.
[002] [LM] A. Lasota and M. C. Mackey, Probabilistic Properties of Deterministic Systems, Cambridge University Press, 1985. | Zbl 0606.58002
[003] [LR] A. Lasota and R. Rudnicki, Asymptotic behaviour of semigroups of positive operators on C(X), Bull. Polish Acad. Sci. Math. 36 (1988), 151-159. | Zbl 0676.47021
[004] [LY] A. Lasota and J. A. Yorke, Exact dynamical systems and the Frobenius-Perron operator, Trans. Amer. Math. Soc. 273 (1982), 375-384. | Zbl 0524.28021
[005] [LY1] A. Lasota and J. A. Yorke, When the long-time behavior is independent of the initial density, SIAM J. Math. Anal. 27 (1996), 221-240. | Zbl 0846.47005
[006] [ŁR] K. Łoskot and R. Rudnicki, Relative entropy and stability of stochastic semigroups, Ann. Polon. Math. 53 (1991), 139-145. | Zbl 0727.60035
[007] [N] R. D. Nussbaum, Eigenvectors of nonlinear positive operators and the linear Krein-Rutman theorem, in: Fixed Point Theory, Proc. Conf. Sherbrooke, Lecture Notes Math. 886, Springer, 1980, 309-330.
[008] [R] R. Rudnicki, Asymptotic properties of the iterates of positive operators on C(X), Bull. Polish Acad. Sci. Math. 34 (1986), 181-187. | Zbl 0604.47018
[009] [S] H. H. Schaefer, Banach Lattices and Positive Operators, Grundlehren Math. Wiss. 215, Springer, 1974. | Zbl 0296.47023
[010] [Y] J. A. Yorke, A certain example of nonnegative operators on the space of all integrable functions on [0,3], unpublished.
[011] [ZKP] P. P. Zabreĭko, M. A. Krasnosel'skiĭ and Yu. V. Pokornyĭ, A certain class of positive linear operators, Funktsional. Anal. i Prilozhen. 5 (4) (1971), 9-17 (in Russian).
[012] [Z] A. Zalewska-Mitura, A generalization of the lower bound function theorem for Markov operators, Univ. Iagell. Acta Math. 1994 (31), 79-85.