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HYPERCYCLICITY OF WEIGHTED COMPOSITION OPERATORS ON THE UNIT BALL OF C^N

Ze-Hua Zhou|Ren-Yu Chen
대한수학회 (The Korean Mathematical Society)|2011.09|대한수학회지 (Journal of the KMS)|제48권 제5호|pp. 969-984

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참고문헌

키워드

weighted composition operatorhypercyclic operatorlinear fractional mapgeneralized Cayley transformHeisenberg transformDenjoy-Wollf point
주제분류수학

초록

This paper discusses the hypercyclicity of weighted composi-tion operators acting on the space of holomorphic functions on the open unit ball B_N of C^N. Several analytic properties of linear fractional self-maps of B_N are given. According to these properties, a few necessary conditions for a weighted composition operator to be hypercyclic in the space of holomorphic functions are proved. Besides, the hypercyclicity of adjoint of weighted composition operators are studied in this paper.

Abstract

This paper discusses the hypercyclicity of weighted composi-tion operators acting on the space of holomorphic functions on the open unit ball B_N of C^N. Several analytic properties of linear fractional self-maps of B_N are given. According to these properties, a few necessary conditions for a weighted composition operator to be hypercyclic in the space of holomorphic functions are proved. Besides, the hypercyclicity of adjoint of weighted composition operators are studied in this paper.

참고문헌 (24)

  1. F. Bayart, "class of linear fractional maps of the ball and their composition operators", Adv. Math, 209(2), pp.649~665 (2007)
  2. C. Bisi, "Linear fractional maps of the unit ball: A geometric study", Adv. Math, 167(2), pp.265~287 (2002)
  3. P. S. Bourdon, "Cyclic composition operators on H2, Operator theory: operator algebras and applications, Part 2", Proc. Sympos. Pure Math, pp.43~53 (1990), Amer. Math. Soc
  4. P. S. Bourdon, "Cyclic phenomena for composition operators", Mem. Amer. Math. Soc, 125(596), pp.105~ (1997)
  5. F. Bracci, "Classication of semigroups of linear fractional maps in the unit ball", Adv. Math, 208(1), pp.318~350 (2007)
  6. K. C. Chan, "The cyclic behavior of translation operators on Hilbert spaces of entire functions", Indiana Univ. Math. J, 40(4), pp.1421~1449 (1991)
  7. X. Chen, "Inner functions and cyclic composition operators on H2(Bn)", J. Math. Anal. Appl, 250(2), pp.660~669 (2000)
  8. J. B. Conway, "Function of One Complex Variable" (1973), Springer-Verlag
  9. C. C. Cowen, "Composition Operators on Spaces of Analytic Func- tions" (1995), CRC Press
  10. C. C. Cowen, "Linear fractional maps of the ball and their composition operators", Acta Sci. Math, 66(1), pp.351~376 (2000)
  11. N. S. Feldman, "The dynamics of cohyponormal operators, Trends in Banach spaces and operator theory", Proc. Conf., Memphis, pp.71~85 (2001)
  12. R. M. Gethner, "Universal vectors for operators on spaces of holomor- phic functions", Proc. Amer. Math. Soc, 100(2), pp.281~288 (1987)
  13. G. Godefroy, "Operators with dense invariant cyclic vector manifolds", J. Funct. Anal, 98(2), pp.229~269 (1991)
  14. K. G. Grosse-Erdmann, "Universal families and hypercyclic operators", Bull. Amer. Math. Soc, 36(3), pp.345~381 (1999)
  15. K. G. Grosse-Erdmann, "Recent developments in hypercyclicity", Rev. R. Acad. Cien. Serie A. Mat, 97(2), pp.273~286 (2003)
  16. L. Jiang, "Cyclic behavior of linear fractional composition operators in the unit ball of CN", J. Math. Anal. Appl, 341(1), pp.601~612 (2008)
  17. C. Kitai, "Invariant closed sets for linear operators" (1982), Univ. of Toronto
  18. B. D. MacCluer, "Iterates of holomorphic self-maps of the unit ball in CN", Michigan Math. J, 30(1), pp.97~106 (1983)
  19. S. Rolewicz, "On orbits of elements", Studia Math, 32, pp.17~22 (1969)
  20. W. Rudin, "Function Theory in the Unit Ball of Cn, Grundlehren Math. Wiss. vol. 241" (1980), Springer-Verlag
  21. H. N. Salas, "Hypercyclic weighted shifts", Trans. Amer. Math. Soc, 347(3), pp.993~1004 (1995)
  22. B. Youse, "Hypercyclic property of weighted composition operators", Proc. Amer. Math. Soc, 135(10), pp.3263~3271 (2007)
  23. B. Youse, "Some necessary and sufficient conditions for Hypercyclicity Criterion", Proc. Indian Acad. Sci. Math. Sci, 115(2), pp.209~216 (2005)
  24. K. Zhu, "Spaces of Holomorphic functions in the Unit Ball, Graduate Texts in Mathe- matics, 226" (2005), Springer-Verlag

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