Turkish Journal of Mathematics
Abstract
Let $X$ be a complex topological vector space with $dim(X)>1$ and $\mathcal{B}(X)$ the set of all continuous linear operators on $X$. The concept of hypercyclicity for a subset of $\mathcal{B}(X)$ was introduced in [1]. In this work, we introduce the notion of hypercyclic criterion for a subset of $\mathcal{B}(X)$. We extend some results known for a single operator and $C_0$-semigroup to a subset of $\mathcal{B}(X)$ and we give applications for $C$-regularized groups of operators.
DOI
10.3906/mat-1808-129
Keywords
Orbit, hypercyclic sets of operators, hypercyclic Operators, $C_0$-semigroup, $C$-regularized group
First Page
402
Last Page
411
Recommended Citation
AMOUCH, M, & BENCHIHEB, O (2019). On linear dynamics of sets of operators. Turkish Journal of Mathematics 43 (1): 402-411. https://doi.org/10.3906/mat-1808-129
