Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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HYPERCYCLIC OPERATOR WEIGHTED SHIFTS

  • Hazarika, Munmun (Department of Mathematical Sciences, Tezpur University) ;
  • Arora, S.C. (Department of Mathematics, University of Delhi)
  • Published : 2004.11.01
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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.

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References

  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

Cited by

  1. HEREDITARILY HYPERCYCLICITY AND SUPERCYCLICITY OF WEIGHTED SHIFTS vol.51, pp.2, 2014, https://doi.org/10.4134/JKMS.2014.51.2.363
  2. Disjoint hypercyclic weighted pseudo-shifts on Banach sequence spaces vol.69, pp.3, 2018, https://doi.org/10.1007/s13348-018-0216-z