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## Hypercyclic Weighted Composition Operators on ℓ^2 (Z)

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A bounded linear operator T on a separable Hilbert space H is called hypercyclic if there exists a vector x ∈ H whose orbit {T n x : n ∈ N} is dense in H . In this paper, we characterize the hypercyclicity of the weighted composition operators Cu,ϕ on ℓ 2 (Z) in terms of their weight functions and symbols. First, a necessary and sufficient condition is given for Cu,ϕ to be hypercyclic. Then, it is shown that the finite direct sums of the hypercyclic weighted composition operators are also hypercyclic. In particular, we conclude that the class of the hypercyclic weighted composition operators is weakly mixing. Finally, several examples are presented to illustrate the hypercyclicity of the weighted composition operators.

Hypercyclic operators, Orbit, Weighted composition operators
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Subjects Engineering Articles Author: Mohammad Reza Azimi
 Bibtex @research article { cankujse368699, journal = {Cankaya University Journal of Science and Engineering}, issn = {1309-6788}, eissn = {2564-7954}, address = {Cankaya University}, year = {2017}, volume = {14}, pages = { - }, doi = {}, title = {Hypercyclic Weighted Composition Operators on ℓ\^2 (Z)}, key = {cite}, author = {Azimi, Mohammad Reza} } APA Azimi, M . (2017). Hypercyclic Weighted Composition Operators on ℓ^2 (Z). Cankaya University Journal of Science and Engineering, 14 (2), . Retrieved from http://dergipark.gov.tr/cankujse/issue/33106/368699 MLA Azimi, M . "Hypercyclic Weighted Composition Operators on ℓ^2 (Z)". Cankaya University Journal of Science and Engineering 14 (2017): Chicago Azimi, M . "Hypercyclic Weighted Composition Operators on ℓ^2 (Z)". Cankaya University Journal of Science and Engineering 14 (2017): RIS TY - JOUR T1 - Hypercyclic Weighted Composition Operators on ℓ^2 (Z) AU - Mohammad Reza Azimi Y1 - 2017 PY - 2017 N1 - DO - T2 - Cankaya University Journal of Science and Engineering JF - Journal JO - JOR SP - EP - VL - 14 IS - 2 SN - 1309-6788-2564-7954 M3 - UR - Y2 - 2019 ER - EndNote %0 Cankaya University Journal of Science and Engineering Hypercyclic Weighted Composition Operators on ℓ^2 (Z) %A Mohammad Reza Azimi %T Hypercyclic Weighted Composition Operators on ℓ^2 (Z) %D 2017 %J Cankaya University Journal of Science and Engineering %P 1309-6788-2564-7954 %V 14 %N 2 %R %U ISNAD Azimi, Mohammad Reza . "Hypercyclic Weighted Composition Operators on ℓ^2 (Z)". Cankaya University Journal of Science and Engineering 14 / 2 (November 2017): -.