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http://dx.doi.org/10.4134/CKMS.c200118

ON MULTI SUBSPACE-HYPERCYCLIC OPERATORS  

Moosapoor, Mansooreh (Department of Mathematics Farhangian University)
Publication Information
Communications of the Korean Mathematical Society / v.35, no.4, 2020 , pp. 1185-1192 More about this Journal
Abstract
In this paper, we introduce and investigate multi subspace-hypercyclic 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 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;
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1 N. Bamerni, V. Kadets, and A. Kilicman, Hypercyclic operators are subspace hypercyclic, J. Math. Anal. Appl. 435 (2016), no. 2, 1812-1815. https://doi.org/10.1016/j.jmaa.2015.11.015   DOI
2 N. Bamerni and A. Kilicman, On subspace-diskcyclicity, Arab J. Math. Sci. 23 (2017), no. 2, 133-140. https://doi.org/10.1016/j.ajmsc.2016.06.001   DOI
3 P. S. Bourdon and N. S. Feldman, Somewhere dense orbits are everywhere dense, Indiana Univ. Math. J. 52 (2003), no. 3, 811-819. https://doi.org/10.1512/iumj.2003.52.2303
4 G. Godefroy and J. H. Shapiro, Operators with dense, invariant, cyclic vector manifolds, J. Funct. Anal. 98 (1991), no. 2, 229-269. https://doi.org/10.1016/0022-1236(91)90078-J   DOI
5 K.-G. Grosse-Erdmann and A. Peris Manguillot, Linear Chaos, Universitext, Springer, London, 2011. https://doi.org/10.1007/978-1-4471-2170-1
6 D. A. Herrero, Hypercyclic operators and chaos, J. Operator Theory 28 (1992), no. 1, 93-103.
7 R. R. Jimenez-Munguia, R. A. Martinez-Avendano, and A. Peris, Some questions about subspace-hypercyclic operators, J. Math. Anal. Appl. 408 (2013), no. 1, 209-212. https://doi.org/10.1016/j.jmaa.2013.05.068   DOI
8 C. M. Le, On subspace-hypercyclic operators, Proc. Amer. Math. Soc. 139 (2011), no. 8, 2847-2852. https://doi.org/10.1090/S0002-9939-2011-10754-8   DOI
9 B. F. Madore and R. A. Martinez-Avendano, Subspace hypercyclicity, J. Math. Anal. Appl. 373 (2011), no. 2, 502-511. https://doi.org/10.1016/j.jmaa.2010.07.049   DOI
10 R. A. Martinez-Avendano and O. Zatarain-Vera, Subspace hypercyclicity for Toeplitz operators, J. Math. Anal. Appl. 422 (2015), no. 1, 772-775. https://doi.org/10.1016/j.jmaa.2014.08.038   DOI
11 V. G. Miller, Remarks on finitely hypercyclic and finitely supercyclic operators, Integral Equations Operator Theory 29 (1997), no. 1, 110-115. https://doi.org/10.1007/BF01191482   DOI
12 M. Moosapoor, Common subspace-hypercyclic vectors, Int. J. Pure Apll. Math. 118 (2018), no. 4, 865-870.
13 A. Peris, Multi-hypercyclic operators are hypercyclic, Math. Z. 236 (2001), no. 4, 779-786. https://doi.org/10.1007/PL00004850   DOI
14 R. A. Martinez-Avendano and P. Rosenthal, An Introduction to Operators on the Hardy-Hilbert Space, Graduate Texts in Mathematics, 237, Springer, New York, 2007.