Three results in linear dynamics

Mohammad  Ansari

doi:10.5269/bspm.64644

Mohammad Ansari https://orcid.org/0000-0002-4688-7335

Abstract

In this article, first we show that the Fr$\acute{\textnormal{e}}$chet space $H(\Bbb D)$ cannot support strongly supercyclic weighted composition operators. Then we compute the constant $\epsilon$ for weighted backward shifts on $\ell^p$ ($1\le p<\infty$) and $c_0$. This constant is used to find strongly hypercyclic scalar multiples of non-invertible strongly supercyclic Banach space operators. Finally, we give an affirmative answer to a recent open question concerning supercyclic vectors.

Downloads

Download data is not yet available.

References

Ansari, M., Supercyclic vectors of operators on normed linear spaces, preprint, https://arxiv.org/abs/2206.01508.

Ansari, M., Strong topological transitivity of some classes of operators, Bull. Belg. Math. Soc. Simon Stevin, 25, 677-685, (2018).

Ansari, M., Hedayatian, K., Khani-Robati, B., Strong hypercyclicity of Banach space operators, J. Korean Math. Soc. 58 (1), 91-107, (2021).

Bamerni, N., Kadets, V., Kilicman, A., Hypercyclic operators are subspace hypercyclic, J. Math. Anal. Appl. 435, 1812-1815, (2016).

Bayart, F., Matheron, E., Dynamics of linear operators, Cambridge University Press, 179, (2009).

Bernal-Gonzalez, L., Bonilla, A., Total and non-total suborbits for hypercyclic operators, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 117, 17, (2023).

Bourdon, P.S., Invertible weighted composition operators, Proc. Amer. Math. Soc. 142 ,289-299, (2014).

Faghih-Ahmadi, M., Hedayatian, K., A note on supercyclic vectors of Hilbert space operators, J. Math. Anal. Appl. 505 (2022).

Grosse-Erdmann, K.-G., Peris Manguillot, A., Linear chaos, Universitext, Springer-Verlag London Limited, (2011).

Rudin, W., Real and complex analysis, McGraw-Hill International Editions, (1987).

Yousefi, B., Rezaei, H., Hypercyclic property of weighted composition operators, Proc. Amer. Math. Soc. 135(10), 3263–3271, (2007).