{'fraction_non_alphanumeric': 0.02937420178799489, 'fraction_numerical': 0.002554278416347382, 'mean_word_length': 4.764705882352941, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Hypercyclic Weighted Composition Operators on ℓ^2 (Z)

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.