## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Non-Weakly Supercyclic Classes of Weighted Composition Operators on Banach Spaces of Analytic Functions

#### Abstract

We present a non-weak supercyclicity criterion for vectors in infinite dimensional Banach spaces. Also, we give sufficient conditions under which a class of weighted composition operators on a Banach space of analytic functions is not weakly supercyclic. In particular, we show that the semigroup of linear isometries on the spaces $S^p$ ($p>1$), is not weakly supercyclic. Moreover, we observe that every composition operator on some Banach space of analytic functions such as the disc algebra or the analytic Lipschitz space is not weakly supercyclic.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 24, Number 2 (2017), 227-241.

Dates
First available in Project Euclid: 23 August 2017

https://projecteuclid.org/euclid.bbms/1503453707

Digital Object Identifier
doi:10.36045/bbms/1503453707

Mathematical Reviews number (MathSciNet)
MR3694000

Zentralblatt MATH identifier
06850668

#### Citation

Moradi, A.; Khani Robati, B.; Hedayatian, K. Non-Weakly Supercyclic Classes of Weighted Composition Operators on Banach Spaces of Analytic Functions. Bull. Belg. Math. Soc. Simon Stevin 24 (2017), no. 2, 227--241. doi:10.36045/bbms/1503453707. https://projecteuclid.org/euclid.bbms/1503453707