Disjoint Ces$\grave{a}$ro-hypercyclic operators

Abstract

In this paper, we investigate the properties of disjoint Ces$\grave{a}$ro-hypercyclic operators. First, the definition of disjoint Ces$\grave{a}$ro-hypercyclic operators is provided, and disjoint Ces$\grave{a}$ro-Hypercyclicity Criterion is proposed. Later, two methods are used to prove that operators satisfying this criterion possess disjoint Ces$\grave{a}$ro-hypercyclicity. Finally, this paper further investigates weighted shift operators and provides detailed characterizations of the weight sequences for disjoint Ces$\grave{a}$ro-hypercyclic unilateral and bilateral weighted shift operators on sequence spaces.

revise example space(example 1.1, 1.2, 1.3), definition 3.4 adds a condition that the sequence $(n_k)$ is increasing, theorem 4.1(complex scalar field)