Mathematische Zeitschrift

, Volume 249, Issue 1, pp 85–96

Topologically transitive extensions of bounded operators


DOI: 10.1007/s00209-004-0690-8

Cite this article as:
Grivaux, S. Math. Z. (2005) 249: 85. doi:10.1007/s00209-004-0690-8


Let X be any Banach space and T a bounded operator on X. An extension of the pair (X,T) consists of a Banach space in which X embeds isometrically through an isometry i and a bounded operator on such that When X is separable, it is additionally required that be separable. We say that is a topologically transitive extension of (X, T) when is topologically transitive on, i.e. for every pair of non-empty open subsets of there exists an integer n such that is non-empty. We show that any such pair (X,T) admits a topologically transitive extension, and that when H is a Hilbert space, (H,T) admits a topologically transitive extension where is also a Hilbert space. We show that these extensions are indeed chaotic.

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Équipe d’AnalyseUniversité Paris 6, Case 186Paris Cedex 05France