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

top
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

top

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

top
  1. [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. [2] J. Appell and P. P. Zabreĭko, Analytic superposition operators, Dokl. Akad. Nauk BSSR 29 (1985), 878-881 (in Russian). Zbl0591.47048
  3. [3] K. Goebel and W. A. Kirk, Topics in Metric Fixed Point Theory, Cambridge Univ. Press, Cambridge, 1990. Zbl0708.47031
  4. [4] P. R. Halmos, Lectures in Ergodic Theory, Chelsea, New York, 1956. 
  5. [5] G. H. Hardy, J. E. Littlewood and G. Pólya, Inequalities, Cambridge Univ. Press, Cambridge, 1934. 
  6. [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. [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. [8] W. A. J. Luxemburg and A. C. Zaanen, Riesz Spaces I, North-Holland, Amsterdam, 1974. 
  9. [9] M. Novak, Unions and intersections of families of L p spaces, Math. Nachr. 136 (1988), 241-251. Zbl0667.46021
  10. [10] M. M. Rao and Z. D. Ren, Theory of Orlicz Spaces, M. Dekker, New York, 1991. 
  11. [11] A. Schönhage, Approximationstheorie, de Gruyter, Berlin, 1971. 
  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. 
  15. [15] E. Zeidler, Nonlinear Functional Analysis and its Applications I, Springer, Berlin, 1990. Zbl0684.47029
  16. [16] K. Zhu, Operator Theory in Function Spaces, M. Dekker, New York, 1990. 

NotesEmbed ?

top

You must be logged in to post comments.

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

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.