Codiskcyclic sets of operators on complex topological vector spaces

TL;DR

This paper extends the concept of codiskcyclicity from individual operators to sets of operators on complex topological vector spaces, providing new criteria and applying them to $C_0$-semigroups.

Contribution

It introduces the notion of codiskcyclicity for sets of operators, establishes a criterion for this property, and applies it to $C_0$-semigroups.

Findings

Established a codiskcyclicity criterion for sets of operators

Extended the concept of codiskcyclicity to operator sets

Analyzed codiskcyclicity in the context of $C_0$-semigroups

Abstract

Let $X$ be a complex topological vector space and $L(X)$ the set of all continuous linear operators on $X.$ In this paper, we extend the notion of the codiskcyclicity of a single operator $T\in L(X)$ to a set of operators $\Gamma\subset L(X).$ We prove some results for codiskcyclic sets of operators and we establish a codiskcyclicity criterion. As an application, we study the codiskcyclicity of $C_0$-semigroups of operators.