Annals of Functional Analysis

Notes about subspace-supercyclic operators

Liang Zhang and Ze-Hua Zhou

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


A bounded linear operator $T$ on a Banach space $X$ is called subspace-hypercyclic for a nonzero subspace $M$ if $orb\left( {T,x} \right) \cap M$ is dense in $M$ for a vector $x \in X$, where $orb (T,x)=\{T^nx: n=0,1,2,\cdots\}$. Similarly, the bounded linear operator $T$ on a Banach space $X$ is called subspace-supercyclic for a nonzero subspace $M$ if there exists a vector whose projective orbit intersects the subspace $M$ in a relatively dense set. In this paper we provide a Subspace-Supercyclicity Criterion and offer two equivalent conditions of this criterion. At the same time, we also characterize other properties of subspace-supercyclic operators.

Article information

Ann. Funct. Anal., Volume 6, Number 2 (2015), 60-68.

First available in Project Euclid: 19 December 2014

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47A16: Cyclic vectors, hypercyclic and chaotic operators
Secondary: 46E15: Banach spaces of continuous, differentiable or analytic functions

Subspace-supercyclic Subspace-Supercyclicity Criterion Banach space


Zhang, Liang; Zhou, Ze-Hua. Notes about subspace-supercyclic operators. Ann. Funct. Anal. 6 (2015), no. 2, 60--68. doi:10.15352/afa/06-2-6.

Export citation


  • P.S. Bourdon, Orbits of hyponormal operators, Michigan Math. J. 44 (1997), 345–353.
  • T. Bermúdez, A. Bonilla and A. Peris, On hypercyclicity and supercyclicity criteria, Bull. Austral. Math. Soc. 70 (2004), no. 1, 45–54.
  • F. Bayart and E. Matheron, Dynamics of Linear Operators, Cambridge University Press, 2009.
  • N. Feldman, V. Miller and L. Miller, Hypercyclic and supercyclic cohyponormal operators, Acta Sci. Math. 68 (2002), 303–328.
  • K.G. Grosse-Erdmann and A. Peris Manguillot, Linear Chaos, Springer, New York, 2011.
  • H.M. Hilden and L.J. Wallen, Some cyclic and non-cyclic vectors of certain operator, Indiana Univ. Math. J. 23 (1974), 557–565.
  • R.R. Jiménez-Munguía, R.A. Martínez-Avendaño and A. Peris, Some questions about subspace-hypercyclic operators, J. Math. Anal. Appl. 408 (2013), no. 1, 209–212.
  • C.M. Le, On subspace-hypercyclicity operators, Proc. Amer. Math. Soc. 139 (2011), no. 8, 2847–2852.
  • B.F. Madore and R.A. Martínez-Avendaño, Subspace hypercyclicity, J. Math. Anal. Appl. 373 (2011), no. 2, 502–511.
  • A. Montes-Rodríguez and H. Salas, Supercyclic subspaces: spectral theory and weighted shifts, Adv. Math. 163 (2001), 74–134.
  • H. Rezaei, Notes on subspace-hypercyclic operators, J. Math. Anal. Appl. 397 (2013), 428–433.
  • H.N. Salas, Supercyclicity and weighted shifts, Studia Math. 135 (1999), no. 1, 55–74.
  • X.F. Zhao, Y.L. Sun and Y.H. Zhou, subspace-supercyclicity and common subspace-supercyclic vectors, J. East China Norm. Univ. Natur. Sci. Ed. 2012 (2012), no. 1, 107–112.