On multi subspace-hypercyclic operators
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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.
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.
참고문헌 (14)
- N. Bamerni, "Hypercyclic operators are subspace hypercyclic", J. Math. Anal. Appl, 435(2), pp.1812~1815 (2016)[DOI]
- N. Bamerni, "On subspace-diskcyclicity", Arab J. Math. Sci, 23(2), pp.133~140 (2017)[DOI]
- P. S. Bourdon, "Somewhere dense orbits are everywhere dense", Indiana Univ. Math. J, 52(3), pp.811~819 (2003)[DOI]
- G. Godefroy, "Operators with dense, invariant, cyclic vector manifolds", J. Funct. Anal, 98(2), pp.229~269 (1991)[DOI]
- K. -G. Grosse-Erdmann, "Linear Chaos, Universitext" (2011), Springer
- D. A. Herrero, "Hypercyclic operators and chaos", J. Operator Theory, 28(1), pp.93~103 (1992)
- R. R. Jim´enez-Mungu´ıa, "Some questions about subspace-hypercyclic operators", J. Math. Anal. Appl, 408(1), pp.209~212 (2013)[DOI]
- C. M. Le, "On subspace-hypercyclic operators", Proc. Amer. Math. Soc, 139(8), pp.2847~2852 (2011)[DOI]
- B. F. Madore, "Subspace hypercyclicity", J. Math. Anal. Appl, 373(2), pp.502~511 (2011)[DOI]
- R. A. Mart´ınez-Avenda˜no, "An Introduction to Operators on the HardyHilbert Space" (2007), Springer
- R. A. Mart´ınez-Avenda˜no, "Subspace hypercyclicity for Toeplitz operators", J. Math. Anal. Appl, 422(1), pp.772~775 (2015)[DOI]
- V. G. Miller, "Remarks on finitely hypercyclic and finitely supercyclic operators", Integral Equations Operator Theory, 29(1), pp.110~115 (1997)[DOI]
- M. Moosapoor, "Common subspace-hypercyclic vectors", Int. J. Pure Apll. Math, 118(4), pp.865~870 (2018)
- A. Peris, "Multi-hypercyclic operators are hypercyclic", Math. Z, 236(4), pp.779~786 (2001)[DOI]