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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