# Some remarks on the asymptotic behaviour of the iterates of a bounded linear operator

Anatoliĭ Antonevich; Jürgen Appell; Petr Zabreĭko

Studia Mathematica (1994)

- Volume: 112, Issue: 1, page 1-11
- ISSN: 0039-3223

## Access Full Article

top## Abstract

top## How to cite

topAntonevich, Anatoliĭ, Appell, Jürgen, and Zabreĭko, Petr. "Some remarks on the asymptotic behaviour of the iterates of a bounded linear operator." Studia Mathematica 112.1 (1994): 1-11. <http://eudml.org/doc/216135>.

@article{Antonevich1994,

abstract = {We discuss the problem of characterizing the possible asymptotic behaviour of the norm of the iterates of a bounded linear operator between two Banach spaces. In particular, given an increasing sequence of positive numbers tending to infinity, we construct Banach spaces such that the norm of the iterates of a suitable multiplication operator between these spaces assumes (or exceeds) the values of this sequence.},

author = {Antonevich, Anatoliĭ, Appell, Jürgen, Zabreĭko, Petr},

journal = {Studia Mathematica},

keywords = {asymptotic behaviour of the norm of the iterates of a bounded linear operator between two Banach spaces; multiplication operator},

language = {eng},

number = {1},

pages = {1-11},

title = {Some remarks on the asymptotic behaviour of the iterates of a bounded linear operator},

url = {http://eudml.org/doc/216135},

volume = {112},

year = {1994},

}

TY - JOUR

AU - Antonevich, Anatoliĭ

AU - Appell, Jürgen

AU - Zabreĭko, Petr

TI - Some remarks on the asymptotic behaviour of the iterates of a bounded linear operator

JO - Studia Mathematica

PY - 1994

VL - 112

IS - 1

SP - 1

EP - 11

AB - We discuss the problem of characterizing the possible asymptotic behaviour of the norm of the iterates of a bounded linear operator between two Banach spaces. In particular, given an increasing sequence of positive numbers tending to infinity, we construct Banach spaces such that the norm of the iterates of a suitable multiplication operator between these spaces assumes (or exceeds) the values of this sequence.

LA - eng

KW - asymptotic behaviour of the norm of the iterates of a bounded linear operator between two Banach spaces; multiplication operator

UR - http://eudml.org/doc/216135

ER -

## References

top- [1] J. Appell and P. P. Zabreĭko, On analyticity conditions for the superposition operator in ideal function spaces, Boll. Un. Mat. Ital. 4-C (1985), 279-295. Zbl0583.47057
- [2] J. Appell and P. P. Zabreĭko, Analytic superposition operators, Dokl. Akad. Nauk BSSR 29 (1985), 878-881 (in Russian). Zbl0591.47048
- [3] K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Univ. Press, Cambridge, 1990. Zbl0708.47031
- [4] P. R. Halmos, Lectures in Ergodic Theory, Chelsea, New York, 1956.
- [5] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, Cambridge, 1934.
- [6] M. A. Krasnosel'skiĭ and Ya. B. Rutitskiĭ, Convex Functions and Orlicz Spaces, Fizmatgiz, Moscow, 1958 (in Russian); English transl.: Noordhoff, Groningen, 1961.
- [7] M. A. Krasnosel'skiĭ and P. P. Zabreĭko, Geometrical Methods of Nonlinear Analysis, Nauka, Moscow, 1975 (in Russian); English transl.: Springer, Berlin, 1984.
- [8] W. A. J. Luxemburg and A. C. Zaanen, Riesz Spaces I, North-Holland, Amsterdam, 1974.
- [9] M. Novak, Unions and intersections of families of ${L}^{p}$ spaces, Math. Nachr. 136 (1988), 241-251. Zbl0667.46021
- [10] M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, M. Dekker, New York, 1991.
- [11] A. Schönhage, Approximationstheorie, de Gruyter, Berlin, 1971.
- [12] P. P. Zabreĭko, Ideal function spaces, Yaroslavl. Gos. Univ. Vestnik 8 (1974), 12-52 (in Russian).
- [13] P. P. Zabreĭko, Error estimates for successive approximations and spectral properties of linear operators, Numer. Funct. Anal. Optim. 11 (1990), 823-838.
- [14] P. P. Zabreĭko, A. I. Koshelev, M. A. Krasnosel'skiĭ, S. G. Mikhlin, L. S. Rakovshchik and V. Ya. Stetsenko, Integral Equations, Nauka, Moscow, 1968 (in Russian); English transl.: Noordhoff, Leyden, 1975.
- [15] E. Zeidler, Nonlinear Functional Analysis and its Applications I, Springer, Berlin, 1990. Zbl0684.47029
- [16] K. Zhu, Operator Theory in Function Spaces, M. Dekker, New York, 1990.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.