Non supercyclic subsets of linear isometries on Banach spaces of analytic functions

Abbas Moradi; Karim Hedayatian; Bahram Khani Robati; Mohammad Ansari

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 2, page 389-397
  • ISSN: 0011-4642

Abstract

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Let X be a Banach space of analytic functions on the open unit disk and Γ a subset of linear isometries on X . Sufficient conditions are given for non-supercyclicity of Γ . In particular, we show that the semigroup of linear isometries on the spaces S p ( p > 1 ), the little Bloch space, and the group of surjective linear isometries on the big Bloch space are not supercyclic. Also, we observe that the groups of all surjective linear isometries on the Hardy space H p or the Bergman space L a p ( 1 < p < ∞ , p ≠ 2 ) are not supercyclic.

How to cite

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Moradi, Abbas, et al. "Non supercyclic subsets of linear isometries on Banach spaces of analytic functions." Czechoslovak Mathematical Journal 65.2 (2015): 389-397. <http://eudml.org/doc/270095>.

@article{Moradi2015,
abstract = {Let $X$ be a Banach space of analytic functions on the open unit disk and $\Gamma $ a subset of linear isometries on $X$. Sufficient conditions are given for non-supercyclicity of $\Gamma $. In particular, we show that the semigroup of linear isometries on the spaces $S^p$ ($p>1$), the little Bloch space, and the group of surjective linear isometries on the big Bloch space are not supercyclic. Also, we observe that the groups of all surjective linear isometries on the Hardy space $H^p$ or the Bergman space $L^\{p\}_\{a\}$ ($1<p<\infty $, $p\ne 2$) are not supercyclic.},
author = {Moradi, Abbas, Hedayatian, Karim, Khani Robati, Bahram, Ansari, Mohammad},
journal = {Czechoslovak Mathematical Journal},
keywords = {supercyclicity; hypercyclic operator; semigroup; isometry},
language = {eng},
number = {2},
pages = {389-397},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Non supercyclic subsets of linear isometries on Banach spaces of analytic functions},
url = {http://eudml.org/doc/270095},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Moradi, Abbas
AU - Hedayatian, Karim
AU - Khani Robati, Bahram
AU - Ansari, Mohammad
TI - Non supercyclic subsets of linear isometries on Banach spaces of analytic functions
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 2
SP - 389
EP - 397
AB - Let $X$ be a Banach space of analytic functions on the open unit disk and $\Gamma $ a subset of linear isometries on $X$. Sufficient conditions are given for non-supercyclicity of $\Gamma $. In particular, we show that the semigroup of linear isometries on the spaces $S^p$ ($p>1$), the little Bloch space, and the group of surjective linear isometries on the big Bloch space are not supercyclic. Also, we observe that the groups of all surjective linear isometries on the Hardy space $H^p$ or the Bergman space $L^{p}_{a}$ ($1<p<\infty $, $p\ne 2$) are not supercyclic.
LA - eng
KW - supercyclicity; hypercyclic operator; semigroup; isometry
UR - http://eudml.org/doc/270095
ER -

References

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  1. Ansari, S. I., 10.1006/jfan.1995.1036, J. Funct. Anal. 128 (1995), 374-383. (1995) Zbl0853.47013MR1319961DOI10.1006/jfan.1995.1036
  2. Bayart, F., Matheron, É., Dynamics of Linear Operators, Cambridge Tracts in Mathematics 179 Cambridge University Press, Cambridge (2009). (2009) Zbl1187.47001MR2533318
  3. Guerrero, J. Becerra, Rodríguez-Palacios, A., Transitivity of the norm on Banach spaces, Extr. Math. 17 (2002), 1-58. (2002) MR1914238
  4. Bonet, J., Lindström, M., Wolf, E., 10.1090/S0002-9939-08-09631-7, Proc. Am. Math. Soc. 136 (2008), 4267-4273. (2008) Zbl1154.47017MR2431039DOI10.1090/S0002-9939-08-09631-7
  5. Bourdon, P. S., Feldman, N. S., 10.1512/iumj.2003.52.2303, Indiana Univ. Math. J. 52 (2003), 811-819. (2003) Zbl1049.47002MR1986898DOI10.1512/iumj.2003.52.2303
  6. Conejero, J. A., Müller, V., Peris, A., 10.1016/j.jfa.2006.12.008, J. Funct. Anal. 244 (2007), 342-348. (2007) Zbl1123.47010MR2294487DOI10.1016/j.jfa.2006.12.008
  7. Conway, J. B., 10.1007/978-1-4612-6313-5, Graduate Texts in Mathematics 11 Springer, New York (1978). (1978) MR0503901DOI10.1007/978-1-4612-6313-5
  8. Copson, E. T., Asymptotic Expansions, Cambridge Tracts in Mathematics and Mathematical Physics 55 Cambridge University Press, New York (1965). (1965) Zbl0123.26001MR0168979
  9. Fleming, R. J., Jamison, J. E., Isometries on Banach Spaces. Vol. 2: Vector-valued Function Spaces, Monographs and Surveys in Pure and Applied Mathematics 138 Chapman and Hall/CRC, Boca Raton (2007). (2007) MR2361284
  10. Fleming, R. J., Jamison, J. E., Isometries on Banach Spaces. Vol. 1: Function Spaces, Monographs and Surveys in Pure and Applied Mathematics 129 Chapman and Hall/CRC, Boca Raton (2003). (2003) MR1957004
  11. Geng, L.-G., Zhou, Z.-H., Dong, X.-T., Isometric composition operators on weighted Dirichlet-type spaces, J. Inequal. Appl. (electronic only) 2012 (2012), Article No. 23, 6 pages. (2012) Zbl1273.47049MR2916341
  12. Greim, P., Jamison, J. E., Kamińska, A., 10.1017/S0305004100072753, Math. Proc. Camb. Philos. Soc. 116 (1994), 475-488 corrigendum ibid. 121 191 (1997). (1997) MR1291754DOI10.1017/S0305004100072753
  13. Hornor, W., Jamison, J. E., 10.1007/BF01202102, Integral Equations Oper. Theory 41 (2001), 410-425. (2001) Zbl0995.46012MR1857800DOI10.1007/BF01202102
  14. Jarosz, K., 10.1007/BF02767369, Isr. J. Math. 64 (1988), 49-56. (1988) Zbl0682.46010MR0981748DOI10.1007/BF02767369
  15. Kitai, C., Invariant Closed Sets for Linear Operators, ProQuest LLC, Ann Arbor University of Toronto Toronto, Canada (1982). (1982) MR2632793
  16. León-Saavedra, F., Müller, V., 10.1007/s00020-003-1299-8, Integral Equations Oper. Theory 50 (2004), 385-391. (2004) Zbl1079.47013MR2104261DOI10.1007/s00020-003-1299-8
  17. Martín, M. J., Vukotić, D., Isometries of some classical function spaces among the composition operators, Recent Advances in Operator-Related Function Theory, Proc. Conf., Dublin, Ireland, 2004 A. L. Matheson et al. Contemp. Math. 393 American Mathematical Society, Providence (2006), 133-138. (2006) Zbl1121.47018MR2198376
  18. Novinger, W. P., Oberlin, D. M., 10.4153/CJM-1985-005-3, Can. J. Math. 37 (1985), 62-74. (1985) Zbl0581.46045MR0777039DOI10.4153/CJM-1985-005-3
  19. Rolewicz, S., 10.4064/sm-32-1-17-22, Stud. Math. 32 (1969), 17-22. (1969) Zbl0174.44203MR0241956DOI10.4064/sm-32-1-17-22

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