On multi subspace-hypercyclic operators

In this paper, we introduce and investigate multi subspacehypercyclic operators and prove that multi-hypercyclic operators are multi subspace-hypercyclic. We show that if T is M -hypercyclic or multi M -hypercyclic, then Tn is multi M -hypercyclic for any natural number n and by using this result, make some examples of multi subspacehypercyclic operators. We prove that multi M -hypercyclic operators have somewhere dense orbits in M . We show that analytic Toeplitz operators can not be multi subspace-hypercyclic. Also, we state a sufficient condition for coanalytic Toeplitz operators to be multi subspace-hypercyclic.