Browse > Article
http://dx.doi.org/10.4134/BKMS.2004.41.4.589

HYPERCYCLIC OPERATOR WEIGHTED SHIFTS  

Hazarika, Munmun (Department of Mathematical Sciences, Tezpur University)
Arora, S.C. (Department of Mathematics, University of Delhi)
Publication Information
Bulletin of the Korean Mathematical Society / v.41, no.4, 2004 , pp. 589-598 More about this Journal
Abstract
We consider bilateral operator weighted shift T on $L^2$(K) with weight sequence ${[A_{n}]_{n=-{\infty}}}^{\infty}$ of positive invertible diagonal operators on K. We give a characterization for T to be hypercyclic, and show that the conditions are far simplified in case T is invertible.
Keywords
operator weighted shift; hypercyclic operator;
Citations & Related Records
연도 인용수 순위
  • Reference
1 P. S. Bourdon and J. H. Shapiro, Cyclic phenomena for composition operators, Mem. Amer. Math. Soc. 125 (1997)
2 N. S. Feldman,Hypercyclicity and supercyclicity for invertible bilateral weighted shifts,Proc. Amer. Math. Soc. 131 (2003), 479–485
3 R. M. Gethner and J. H. Shapiro,Universal vectors for operators on spaces of holomorphic functions, Proc. Amer. Math. Soc. 100 (1987), 281–288
4 D. A. Herrero,Hypercyclic operators and chaos, J. Operator Theory 28 (1992), 93–103
5 C. Kitai, Invariant closed sets for linear operators, Dissertation, University of Toronto (1982)
6 S. Rolewicz, On orbits of elements,Studia Math. 32 (1969), 17–22
7 H. N. Salas, Hypercyclic weighted shifts, Trans. Amer. Math. Soc. 347 (1995), 993–1004