On multi subspace-hypercyclic operators
Commun. Korean Math. Soc. 2020 Vol. 35, No. 4, 1185-1192
https://doi.org/10.4134/CKMS.c200118
Published online August 27, 2020
Printed October 31, 2020
Mansooreh Moosapoor
Farhangian University
Abstract : 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
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