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Hypercyclic and chaotic weighted shifts

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EN
Extending previous results of H. Salas we obtain a characterisation of hypercyclic weighted shifts on an arbitrary F-sequence space in which the canonical unit vectors $(e_n)$ form a Schauder basis. If the basis is unconditional we give a characterisation of those hypercyclic weighted shifts that are even chaotic.
Twórcy
Bibliografia
  • [1] J. Banks, J. Brooks, G. Cairns, G. Davis and P. Stacey, On Devaney's definition of chaos, Amer. Math. Monthly 99 (1992), 332-334.
  • [2] B. Beauzamy, Introduction to Operator Theory and Invariant Subspaces, North-Holland, Amsterdam, 1988.
  • [3] L. Bernal-González, Derivative and antiderivative operators and the size of complex domains, Ann. Polon. Math. 59 (1994), 267-274.
  • [4] L. Bernal-González, Universal functions for Taylor shifts, Complex Variables Theory Appl. 31 (1996), 121-129.
  • [5] L. Bernal-González and A. Montes-Rodríguez, Universal functions for composition operators, ibid. 27 (1995), 47-56.
  • [6] J. Bès and A. Peris, Hereditarily hypercyclic operators, J. Funct. Anal. 167 (1999), 94-112.
  • [7] G. D. Birkhoff, Démonstration d'un théorème élémentaire sur les fonctions entières, C. R. Acad. Sci. Paris 189 (1929), 473-475.
  • [8] R. L. Devaney, An Introduction to Chaotic Dynamical Systems, Benjamin/Cummings, Menlo Park, CA, 1986.
  • [9] P. L. Duren, Theory of $H^p$ Spaces, Academic Press, New York, 1970.
  • [10] R. M. Gethner and J. H. Shapiro, Universal vectors for operators on spaces of holomorphic functions, Proc. Amer. Math. Soc. 100 (1987), 281-288.
  • [11] G. Godefroy and J. H. Shapiro, Operators with dense invariant cyclic vector manifolds, J. Funct. Anal. 98 (1991), 229-269.
  • [12] K.-G. Grosse-Erdmann, Holomorphe Monster und universelle Funktionen, Mitt. Math. Sem. Giessen 176 (1987).
  • [13] K.-G. Grosse-Erdmann, On the universal functions of G. R. MacLane, Complex Variables Theory Appl. 15 (1990), 193-196.
  • [14] K.-G. Grosse-Erdmann, Universal families and hypercyclic operators, Bull. Amer. Math. Soc. (N.S.) 36 (1999), 345-381.
  • [15] A. Gulisashvili and C. R. MacCluer, Linear chaos in the unforced quantum harmonic oscillator, J. Dynam. Systems Measurement Control 118 (1996), 337-338.
  • [16] D. A. Herrero and Z.-Y. Wang, Compact perturbations of hypercyclic and supercyclic operators, Indiana Univ. Math. J. 39 (1990), 819-829.
  • [17] N. J. Kalton, N. T. Peck and J. W. Roberts, An F-space Sampler, Cambridge Univ. Press, Cambridge, 1984.
  • [18] P. K. Kamthan and M. Gupta, Sequence Spaces and Series, Marcel Dekker, New York, 1981.
  • [19] C. Kitai, Invariant closed sets for linear operators, thesis, Univ. of Toronto, Toronto, 1982.
  • [20] R. deLaubenfels and H. Emamirad, Chaos for functions of discrete and continuous weighted shift operators, preprint.
  • [21] F. León-Saavedra and A. Montes-Rodríguez, Linear structure of hypercyclic vectors, J. Funct. Anal. 148 (1997), 524-545.
  • [22] F. León-Saavedra and A. Montes-Rodríguez, Spectral theory and hypercyclic subspaces, Trans. Amer. Math. Soc., to appear.
  • [23] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces. I, Springer, Berlin, 1977.
  • [24] G. R. MacLane, Sequences of derivatives and normal families, J. Anal. Math. 2 (1952/53), 72-87.
  • [25] F. Martínez-Giménez and A. Peris, Hypercyclic and chaotic backward shift operators on Köthe echelon spaces, preprint.
  • [26] V. Mathew, A note on hypercyclic operators on the space of entire sequences, Indian J. Pure Appl. Math. 25 (1994), 1181-1184.
  • [27] R. I. Ovsepian and A. Pełczyński, On the existence of a fundamental total and bounded biorthogonal sequence in every separable Banach space, and related constructions of uniformly bounded orthonormal systems in $L^2$, Studia Math. 54 (1975), 149-159.
  • [28] A. Peris, Chaotic polynomials on Fréchet spaces, Proc. Amer. Math. Soc. 127 (1999), 3601-3603.
  • [29] S. Rolewicz, On orbits of elements, Studia Math. 32 (1969), 17-22.
  • [30] S. Rolewicz, Metric Linear Spaces, second ed., D. Reidel, Dordrecht, 1985.
  • [31] H. Salas, A hypercyclic operator whose adjoint is also hypercyclic, Proc. Amer. Math. Soc. 112 (1991), 765-770.
  • [32] H. Salas, Hypercyclic weighted shifts, Trans. Amer. Math. Soc. 347 (1995), 993-1004.
  • [33] I. Singer, Bases in Banach Spaces. I, Springer, Berlin, 1970.
  • [34] I. Singer, Bases in Banach Spaces. II, Springer, Berlin, 1981.
  • [35] R. L. Wheeden and A. Zygmund, Measure and Integral, Marcel Dekker, New York, 1977.
  • [36] A. Wilansky, Summability through Functional Analysis, North-Holland, Amsterdam, 1984.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv139i1p47bwm
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