Diskcyclicity of sets of operators and applications

2019/05/11 by Amouch, Mohamed, Benchiheb, Otmane
#47A16 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1905.04507

Abstract

In this paper, we extend the notion of diskcyclicity and disk transitivity of a single operator to a subset of B(X). We establish a diskcyclicity criterion and we give the relationship between this criterion and the diskcyclicity. As applications, we study the diskcyclicty of C₀-semigroups and C-regularized groups of operators. We show that a diskcyclic C₀-semigroup exists on a complex topological vector space X if and only if dim(X)=1 or dim(X)=∞ and we prove that diskcyclicity and disk transitivity of a C₀-semigroups and C-regularized groups are equivalent.

Related

• On Linear Dynamics of Sets of Operators
• On supercyclic sets of operators
• A review of some works in the theory of diskcyclic operators
• On subspaces diskcyclicity
• Codiskcyclic sets of operators on complex topological vector spaces