Dynamics of Generalised Derivations and Elementary Operators
Clifford Gilmore
TL;DR
This paper explores the hypercyclic behavior of generalized derivations and elementary operators on operator ideals and Banach algebras, revealing new instances of complex dynamics in operator theory.
Contribution
It provides concrete examples of hypercyclic generalized derivations and elementary operators, and establishes necessary conditions for their hypercyclicity.
Findings
Hypercyclic generalized derivations identified on separable ideals.
Elementary operators exhibit surprising hypercyclic behavior.
Necessary conditions for hypercyclicity of these operators established.
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.
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