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2000 | 138 | 3 | 241-250
Tytuł artykułu

Universal images of universal elements

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We furnish several necessary and sufficient conditions for the following property: For a topological space X, a continuous selfmapping S of X and a family τ of continuous selfmappings of X, the image under S of every τ-universal element is also τ-universal. An application in operator theory, where we extend results of Bourdon, Herrero, Bes, Herzog and Lemmert, is given. In particular, it is proved that every hypercyclic operator on a real or complex Banach space has a dense invariant linear manifold with maximal algebraic dimension consisting, apart from zero, of vectors which are hypercyclic.
Czasopismo
Rocznik
Tom
138
Numer
3
Strony
241-250
Opis fizyczny
Daty
wydano
2000
otrzymano
1998-09-18
poprawiono
1999-01-22
Twórcy
  • Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, Sevilla 41080, Spain., lbernal@cica.es
Bibliografia
  • [An] S. I. Ansari, Existence of hypercyclic operators on topological vector spaces, J. Funct. Anal. 148 (1997), 384-390.
  • [Be] L. Bernal-González, On hypercyclic operators on Banach spaces, Proc. Amer. Math. Soc. 127 (1999), 1003-1010.
  • [Bs] J. Bes, Invariant manifolds of hypercyclic vectors for the real scalar case, ibid., 1801-1804.
  • [BP] J. Bonet and A. Peris, Hypercyclic operators on non-normable Fréchet spaces, J. Funct. Anal. 159 (1998), 587-596.
  • [Bo] P. S. Bourdon, Invariant manifolds of hypercyclic vectors, Proc. Amer. Math. Soc. 118 (1993), 845-847.
  • [Do] H. R. Dowson, Spectral Theory of Linear Operators, Academic Press, London, 1978.
  • [GS] G. Godefroy and J. H. Shapiro, Operators with dense, invariant, cyclic vector manifolds, J. Funct. Anal. 98 (1991), 229-269.
  • [Gr] K. G. Grosse-Erdmann, Holomorphe Monster und universelle Funktionen, Mitt. Math. Sem. Giessen 176 (1987).
  • [He] D. A. Herrero, Limits of hypercyclic and supercyclic operators, J. Funct. Anal. 99 (1991), 179-190.
  • [HL] G. Herzog und R. Lemmert, Über Endomorphismen mit dichten Bahnen, Math. Z. 213 (1993), 473-477.
  • [HS] G. Herzog and C. Schmoeger, On operators T such that ⨍(T) is hypercyclic, Studia Math. 108 (1994), 209-216.
  • [Ki] C. Kitai, Invariant closed sets for linear operators, Dissertation, University of Toronto, 1982.
  • [Re] C. J. Read, The invariant subspace problem for a class of Banach spaces, 2: hypercyclic operators, Israel J. Math. 63 (1988), 1-40.
  • [Ro] S. Rolewicz, On orbits of elements, Studia Math. 32 (1969), 17-22.
  • [Ru] W. Rudin, Functional Analysis, McGraw-Hill, New York, 1991.
  • [Sc] C. Schmoeger, On the norm-closure of the class of hypercyclic operators, Ann. Polon. Math. 65 (1997), 157-161.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv138i3p241bwm
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