Dynamics of Generalised Derivations and Elementary Operators

Abstract

We identify concrete examples of hypercyclic generalised derivations acting on separable ideals of operators and establish some necessary conditions for their hypercyclicity. We also consider the dynamics of elementary operators acting on particular Banach algebras, which reveals surprising hypercyclic behaviour on the space of bounded linear operators on the Banach space constructed by Argyros and Haydon.

17 pages. Added some minor observations and examples. Corrected some typos

References in corpus (2)

• Hereditarily indecomposable, separable L_\infty spaces with \ell_1 dual having few operators, but not very few operators
• Hypercyclicity Properties of Commutator Maps

Cited by in corpus (1)

• Linear Dynamical Systems