We give sufficient conditions under which a weighted composition operator on a Hilbert space of analytic functions is not weakly supercyclic. Also, we give some necessary and sufficient conditions for hypercyclicity and supercyclicity of weighted composition operators on the space of analytic functions on the open unit disc.

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In this paper, the power boundedness and mean ergodicity of multiplication operators are investigated on the Bloch space B, the little Bloch space B 0 and the Besov Space B p . Let U be the unit disk on the complex plane C and ψ be a function on the space of holomorphic functions H(U), our goal is to find out when the multiplication operator M ψ is power bounded, mean ergodic and uniformly mean ergodic on B, B 0 and B p .

AbstractIn this paper, we discuss the hypercyclic properties of composition operators on Orlicz function spaces. We give some different conditions under which a composition operator on Orlicz spaces is hyper-cyclic or not. Similarly, multiplication operators are considered. It is shown that there is no hypercyclic multiplication operator on Orlicz spaces.