Yao, Yuwu; Chen, Xiu; Niu, Xin The complexity on the family of operators. (English) Zbl 1363.47014 Math. Appl. 29, No. 3, 649-655 (2016). Summary: In this paper the complexity about the family of bounded linear operators is discussed. We first give a characterization about a family of operators on Banach space to have a dense \(G_\delta\) set common hypercyclic vectors. Then as an application, we show that the set of all common hypercyclic vectors for the family \(\{\lambda B: \lambda \in \Lambda\}\) is a dense \(G_\delta\) set, where \(B\) is the unilateral backward shift and \(\Lambda\) is a bounded, closed subset of \(\mathbb{C}\) with \(\lambda \in \Lambda\), \(|\lambda| > 1\). MSC: 47A16 Cyclic vectors, hypercyclic and chaotic operators Keywords:Banach space; hypercyclic operator; backward shift; common hypercyclic vector PDFBibTeX XMLCite \textit{Y. Yao} et al., Math. Appl. 29, No. 3, 649--655 (2016; Zbl 1363.47014)