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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.
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참고문헌 (14)
참고문헌 신청
N. Bamerni / 2016 / Hypercyclic operators are subspace hypercyclic / J. Math. Anal. Appl 435(2):1812~1815
N. Bamerni / 2017 / On subspace-diskcyclicity / Arab J. Math. Sci 23(2):133~140
P. S. Bourdon / 2003 / Somewhere dense orbits are everywhere dense / Indiana Univ. Math. J 52(3):811~819
G. Godefroy / 1991 / Operators with dense, invariant, cyclic vector manifolds / J. Funct. Anal 98(2):229~269
K. -G. Grosse-Erdmann / 2011 / Linear Chaos, Universitext / Springer
N. Bamerni / 2017 / On subspace-diskcyclicity / Arab J. Math. Sci 23(2):133~140
P. S. Bourdon / 2003 / Somewhere dense orbits are everywhere dense / Indiana Univ. Math. J 52(3):811~819
G. Godefroy / 1991 / Operators with dense, invariant, cyclic vector manifolds / J. Funct. Anal 98(2):229~269
K. -G. Grosse-Erdmann / 2011 / Linear Chaos, Universitext / Springer
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