# On linear dynamics of sets of operators

Öz 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.
Anahtar Kelimeler:

## Orbit, hypercyclic sets of operators, hypercyclic Operators, $C_0$-semigroup, $C$-regularized group

#### Kaynak Göster

 Bibtex @ { tbtkmath575271, journal = {Turkish Journal of Mathematics}, issn = {1300-0098}, eissn = {1303-6149}, address = {}, publisher = {TÜBİTAK}, year = {2019}, volume = {43}, pages = {402 - 411}, doi = {}, title = {On linear dynamics of sets of operators}, key = {cite}, author = {Amouch, Mohamed and Benchıheb, Otmane} } APA Amouch, M , Benchıheb, O . (2019). On linear dynamics of sets of operators . Turkish Journal of Mathematics , 43 (1) , 402-411 . MLA Amouch, M , Benchıheb, O . "On linear dynamics of sets of operators" . Turkish Journal of Mathematics 43 (2019 ): 402-411 < Chicago Amouch, M , Benchıheb, O . "On linear dynamics of sets of operators". Turkish Journal of Mathematics 43 (2019 ): 402-411 RIS TY - JOUR T1 - On linear dynamics of sets of operators AU - Mohamed Amouch , Otmane Benchıheb Y1 - 2019 PY - 2019 N1 - DO - T2 - Turkish Journal of Mathematics JF - Journal JO - JOR SP - 402 EP - 411 VL - 43 IS - 1 SN - 1300-0098-1303-6149 M3 - UR - Y2 - 2021 ER - EndNote %0 Turkish Journal of Mathematics On linear dynamics of sets of operators %A Mohamed Amouch , Otmane Benchıheb %T On linear dynamics of sets of operators %D 2019 %J Turkish Journal of Mathematics %P 1300-0098-1303-6149 %V 43 %N 1 %R %U ISNAD Amouch, Mohamed , Benchıheb, Otmane . "On linear dynamics of sets of operators". Turkish Journal of Mathematics 43 / 1 (Şubat 2019): 402-411 . AMA Amouch M , Benchıheb O . On linear dynamics of sets of operators. Turkish Journal of Mathematics. 2019; 43(1): 402-411. Vancouver Amouch M , Benchıheb O . On linear dynamics of sets of operators. Turkish Journal of Mathematics. 2019; 43(1): 402-411. IEEE M. Amouch ve O. Benchıheb , "On linear dynamics of sets of operators", Turkish Journal of Mathematics, c. 43, sayı. 1, ss. 402-411, Şub. 2019