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HEREDITARILY HYPERCYCLICITY AND SUPERCYCLICITY OF WEIGHTED SHIFTS
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 Title & Authors
HEREDITARILY HYPERCYCLICITY AND SUPERCYCLICITY OF WEIGHTED SHIFTS
Liang, Yu-Xia; Zhou, Ze-Hua;
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 Abstract
In this paper we first characterize the hereditarily hypercyclicity of the unilateral (or bilateral) weighted shifts on the spaces (or ) with weight sequence {} of positive invertible diagonal operators on a separable complex Hilbert space . Then we give the necessary and sufficient conditions for the supercyclicity of those weighted shifts, which extends some previous results of H. Salas. At last, we give some conditions for the supercyclicity of three different weighted shifts.
 Keywords
hereditarily hypercyclic;supercyclic;weighted shifts;
 Language
English
 Cited by
1.
Disjoint supercyclic weighted translations generated by aperiodic elements, Collectanea Mathematica, 2016  crossref(new windwow)
2.
Supercyclic translation $C_0$-semigroup on complex sectors, Discrete and Continuous Dynamical Systems, 2015, 36, 1, 361  crossref(new windwow)
 References
1.
F. Bayart and E. Matheron, Dynamics of Linear Operators, Camberidge University Press, 2009.

2.
J. Bes, Hereditarily hypercyclic operators, J. Funct. Anal. 167 (1999), no. 1, 94-112. crossref(new window)

3.
R. Y. Chen and Z. H. Zhou, Hypercyclicity of weighted composition operators on the unit ball of ${\mathbb{C}}^N$, J. Korean Math. Soc. 48 (2011), no. 5, 969-984. crossref(new window)

4.
G. Godefroy and J. H. Shapiro, Operators with dense, invariant, cyclic vector manifolds. J. Funct. Anal. 98 (1991), no. 2, 229-269. crossref(new window)

5.
K. G. Grosse-Erdmann, Hypercyclic and chaotic weighted shifts, Studia Math. 139 (2000), no. 1, 47-68.

6.
K. G. Grosse-Erdmann and A. P. Manguillot, Linear Chaos, Springer, New York, 2011.

7.
M. Hazarika and S. C. Arora, Hypercyclic operator weighted shifts, Bull. Korean Math. Soc. 41 (2004), no. 4, 589-598. crossref(new window)

8.
C. Kitai, Invariant closed sets for linear operators, Phd thesis, Univ. of Toronto, 1982.

9.
S. Rolewicz, On orbits of elements, Studia Math. 32 (1969), 17-22.

10.
H. N. Salas, Hypercyclic weighted shifts, Trans. Amer. Math. Soc. 347 (1995), no. 3, 993-1004. crossref(new window)

11.
H. N. Salas, Supercyclicity and weighted shifts, Studia Math. 135 (1999), no. 1, 55-74.

12.
B. Yousefi and A. Farrokhinia, On the hereditarily hypercyclic operators, J. Korean Math. Soc. 43 (2006), no. 6, 1219-1229. crossref(new window)