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

Abstract

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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.

How to cite

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Antonevich, 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

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  2. [2] J. Appell and P. P. Zabreĭko, Analytic superposition operators, Dokl. Akad. Nauk BSSR 29 (1985), 878-881 (in Russian). Zbl0591.47048
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  12. [12] P. P. Zabreĭko, Ideal function spaces, Yaroslavl. Gos. Univ. Vestnik 8 (1974), 12-52 (in Russian). 
  13. [13] P. P. Zabreĭko, Error estimates for successive approximations and spectral properties of linear operators, Numer. Funct. Anal. Optim. 11 (1990), 823-838. 
  14. [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. 
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