Taiwanese Journal of Mathematics

SUPERCYCLIC AND CESÀRO HYPERCYCLIC WEIGHTED TRANSLATIONS ON GROUPS

Chung-Chuan Chen

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Abstract

Let $G$ be a locally compact group and let $1 \leq p \lt \infty$. We characterize supercyclic weighted translation operators on the Lebesgue space $L^p(G)$ in terms of the weight. Using this result, the characterization for Cesàro hypercyclic weighted translation operators is given. We also determine when scalar multiples of weighted translation operators are hypercyclic and topologically mixing, and show, for any weighted translation operator $T$, $\beta T$ is mixing for all $\beta \in (1,4)$ if $T$ and $4T$ are mixing.

Article information

Source
Taiwanese J. Math., Volume 16, Number 5 (2012), 1815-1827.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406799

Digital Object Identifier
doi:10.11650/twjm/1500406799

Mathematical Reviews number (MathSciNet)
MR2970687

Zentralblatt MATH identifier
1275.47020

Subjects
Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators 47B38: Operators on function spaces (general) 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.

Keywords
supercyclic operators Cesàro hypercyclic operators locally compact groups $L^p$-spaces

Citation

Chen, Chung-Chuan. SUPERCYCLIC AND CESÀRO HYPERCYCLIC WEIGHTED TRANSLATIONS ON GROUPS. Taiwanese J. Math. 16 (2012), no. 5, 1815--1827. doi:10.11650/twjm/1500406799. https://projecteuclid.org/euclid.twjm/1500406799


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