Asymptotic behaviour of the iterates of nonnegative operators on a Banach lattice

Jolanta Socała

Annales Polonici Mathematici (1998)

  • Volume: 68, Issue: 1, page 1-16
  • ISSN: 0066-2216

Abstract

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Asymptotic convergence theorems for nonnegative operators on Banach lattices, on L ∞ , on C(X) and on L p ( 1 ≤ p < ∞ ) are proved. The general results are applied to a class of integral operators on L¹.

How to cite

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Jolanta Socała. "Asymptotic behaviour of the iterates of nonnegative operators on a Banach lattice." Annales Polonici Mathematici 68.1 (1998): 1-16. <http://eudml.org/doc/270372>.

@article{JolantaSocała1998,
abstract = {Asymptotic convergence theorems for nonnegative operators on Banach lattices, on $L^\{∞\}$, on C(X) and on $L^p(1 ≤ p < ∞)$ are proved. The general results are applied to a class of integral operators on L¹.},
author = {Jolanta Socała},
journal = {Annales Polonici Mathematici},
keywords = {nonnegative operator; exponentially stationary operator; integral operator; lower function; asymptotic convergence theorems; nonnegative operators on Banach lattices; integral operators},
language = {eng},
number = {1},
pages = {1-16},
title = {Asymptotic behaviour of the iterates of nonnegative operators on a Banach lattice},
url = {http://eudml.org/doc/270372},
volume = {68},
year = {1998},
}

TY - JOUR
AU - Jolanta Socała
TI - Asymptotic behaviour of the iterates of nonnegative operators on a Banach lattice
JO - Annales Polonici Mathematici
PY - 1998
VL - 68
IS - 1
SP - 1
EP - 16
AB - Asymptotic convergence theorems for nonnegative operators on Banach lattices, on $L^{∞}$, on C(X) and on $L^p(1 ≤ p < ∞)$ are proved. The general results are applied to a class of integral operators on L¹.
LA - eng
KW - nonnegative operator; exponentially stationary operator; integral operator; lower function; asymptotic convergence theorems; nonnegative operators on Banach lattices; integral operators
UR - http://eudml.org/doc/270372
ER -

References

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  9. [R] R. Rudnicki, Asymptotic properties of the iterates of positive operators on C(X), Bull. Polish Acad. Sci. Math. 34 (1986), 181-187. Zbl0604.47018
  10. [S] H. H. Schaefer, Banach Lattices and Positive Operators, Grundlehren Math. Wiss. 215, Springer, 1974. Zbl0296.47023
  11. [Y] J. A. Yorke, A certain example of nonnegative operators on the space of all integrable functions on [0,3], unpublished. 
  12. [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). 
  13. [Z] A. Zalewska-Mitura, A generalization of the lower bound function theorem for Markov operators, Univ. Iagell. Acta Math. 1994 (31), 79-85. 

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