Disjoint supercyclicity in Banach algebras

2025/06/06 by Ivkovic, Stefan
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2506.06529

Abstract

In this paper, we consider operators that are a composition of an isometric isomorphism and a left multiplier on a normed algebra, and we characterize disjoint F-semi-transitive and disjoint supercyclic such operators on a large class of non-unital normed algebras. It turns out that generalized weighted bilateral shifts on the standard Hilbert C*-module are just a special case of our theory. Generalized weighted composition operators on the normed algebra of operator-valued continuous functions vanishing at infinity on a locally compact, non-compact Hausdorff space are another special case of our theory. Also, we illustrate our results with concrete examples.

Citations

• Frequent, disjoint hypercyclicity and strong topological transitivity of generalized weighted shift operators on Hilbert C-modules
• Dynamics on weighted solid Banach function spaces
• Porosity and supercyclic operators on solid Banach function spaces
• Dynamics of operators on the space of Radon measures
• Disjoint hypercyclic weighted pseudo-shift operators generated by different shifts

Related

• Porosity and supercyclic operators on solid Banach function spaces
• Supercyclicity of the left and right multiplication operators on Banach\n ideal of operators
• \mathbb R- and \mathbb C-supercyclicity for some classes of operators
• Disjoint frequent hypercyclicity of composition operators
• Supercyclic weighted composition operators on the space of smooth functions