Bulletin of the Belgian Mathematical Society - Simon Stevin

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

A. Moradi, B. Khani Robati, and K. Hedayatian

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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

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1503453707

Digital Object Identifier
doi:10.36045/bbms/1503453707

Mathematical Reviews number (MathSciNet)
MR3694000

Zentralblatt MATH identifier
06850668

Subjects
Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators 47B33: Composition operators 47B38: Operators on function spaces (general)

Keywords
Weakly supercyclic composition operators semigroup, isometry fixed point

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


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