Spectral characterization of weak topological transitivity

• Autores: W. Desch, W. Schappacher
• Localización: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas ( RACSAM ), ISSN-e 1578-7303, Vol. 105, Nº. 2, 2011, págs. 403-414
• Idioma: inglés
• DOI: 10.1007/s13398-011-0023-9
• Texto completo no disponible (Saber más ...)
• Resumen

  • Given a bounded linear operator S on a real Banach space X, we characterize weak topological transitivity of the operator families {St {pipe} t e{open} ℕ},{St {pipe} t e{open} ℕ,k > 0}, and {St {pipe} t e{open} ℕ,k e{open} ℝ} in terms of the point spectrum of the dual operator S*. © 2011 Springer-Verlag.

• Referencias bibliográficas
  • Ansari, S.I., Hypercyclic and cyclic vectors (1995) J. Funct. Anal., 128, pp. 374-383
  • Bayart, F., Matheron, E., Hypercyclic operators failing the hypercyclicity criterion on classical Banach spaces (2007) J. Funct. Anal., 250,...
  • Bermudez, T., Bonilla, A., Peris, A., ℂ-supercyclic versus ℝ-supercyclic operators (2002) Arch. Math., 79, pp. 125-130
  • Bonet, J., Peris, A., Hypercyclic operators on non-normable Fréchet spaces (1998) J. Funct. Anal., 159, pp. 587-595
  • Bonet, J., Frerick, L., Peris, A., Wengenroth, J., Transitive and hypercyclic operators on locally convex spaces (2005) Bull. Lond. Math....
  • Chan, K., Sanders, R., A weakly hypercyclic operator that is not norm hypercyclic (2004) J. Oper. Theory, 52, pp. 35-59
  • Conejero, J., Müller, V., Peris, A., Hypercyclic behavior of operators in a hypercyclic C0-semigroup (2007) J. Funct. Anal., 244, pp. 342-348
  • Costakis, K., Peris, A., Hypercyclic semigroups and somewhere dense orbits (2002) C. R. Acad. Sci. Paris, Ser I, 335, pp. 895-898
  • de La rosa, M., Notes about weakly hypercyclic operators (2008) J. Oper. Theory, 35 (1), pp. 101-103
  • de La rosa, M., Read, C., A hypercyclic operator whose direct sum T⊕T is not hypercyclic (2009) J. Oper. Theory, 61 (2), pp. 369-380
  • Dilworthy, S.J., Troitsky, V.G., Spectrum of a weakly hypercyclic operator meets the unit circle (2003) Contemp. Math. AMS, 321, pp. 67-69
  • Herrero, D.A., Limits of hypercyclic and supercyclic operators (1991) J. Funct. Anal, 99, pp. 179-190
  • Herzog, G., Lemmert, R., Über Endomorphismen mit dichten Bahnen (1993) Math. Z., 213, pp. 473-477
  • Kitai, C., (1982) Invariant Closed Sets For Linear Operators, , PhD thesis, Toronto
  • Peris, A., Multi-hypercyclic operators are hypercyclic (2001) Math. Z., 236, pp. 779-786
  • Prǎjiturǎ, G., Limits of weakly hypercyclic and supercyclic operators (2005) Glasgow Math. J., 47, pp. 255-260
  • Sanders, R., Weakly supercyclic operators (2004) J. Math. Anal. Appl., 292, pp. 148-159
  • Shkarin, S., (2008) Existence theorems in linear chaos, , arXiv: 0810. 1192v2