Turkish Journal of Mathematics
DOI
10.3906/mat-1808-129
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.
Keywords
Orbit, hypercyclic sets of operators, hypercyclic Operators, $C_0$-semigroup, $C$-regularized group
First Page
402
Last Page
411
Recommended Citation
AMOUCH, MOHAMED and BENCHIHEB, OTMANE
(2019)
"On linear dynamics of sets of operators,"
Turkish Journal of Mathematics: Vol. 43:
No.
1, Article 32.
https://doi.org/10.3906/mat-1808-129
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss1/32
