Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-28T04:09:42.825Z Has data issue: false hasContentIssue false
  • English
  • Français

HYPONORMAL OPERATORS, WEIGHTED SHIFTS AND WEAK FORMS OF SUPERCYCLICITY

Published online by Cambridge University Press:  02 February 2006

Frédéric Bayart  and
Etienne Matheron
Frédéric Bayart
Affiliation:
Laboratoire Bordelais d’Analyse et de Géométrie, UMR 5467, Université Bordeaux 1, 351 Cours de la Libération, 33405 Talence Cedex, France ([email protected]; [email protected])
Etienne Matheron
Affiliation:
Laboratoire Bordelais d’Analyse et de Géométrie, UMR 5467, Université Bordeaux 1, 351 Cours de la Libération, 33405 Talence Cedex, France ([email protected]; [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An operator $T$ on a Banach space $X$ is said to be weakly supercyclic (respectively $N$-supercyclic) if there exists a one-dimensional (respectively $N$-dimensional) subspace of $X$ whose orbit under $T$ is weakly dense (respectively norm dense) in $X$. We show that a weakly supercyclic hyponormal operator is necessarily a multiple of a unitary operator, and we give an example of a weakly supercyclic unitary operator. On the other hand, we show that hyponormal operators are never $N$-supercyclic. Finally, we characterize $N$-supercyclic weighted shifts.

Keywords

Primary 47A1647B2043A46hypercyclicsupercyclichyponormal operatorsweighted shiftsKronecker sets
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 1 , February 2006 , pp. 1 - 15
Copyright
Copyright © Edinburgh Mathematical Society 2006