Communications of the
Korean Mathematical Society CKMS

In this paper, we introduce and investigate multi subspace-hypercyclic operators and prove that multi-hypercyclic operators are \linebreak multi subspace-hypercyclic. We show that if $T$ is $M$-hypercyclic or multi $M$-hypercyclic, then $T^{n}$ is multi $M$-hypercyclic for any natural number $n$ and by using this result, make some examples of multi subspace-hypercyclic 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.

Keywords: Subspace-hypercyclic operators, multi-hypercyclic operators, multi subspace-hypercyclic operators, Toeplitz operators

MSC numbers: Primary 47A16, 47B37, 37B99