Skip to main content
Log in

Supercyclicity in the operator algebra using Hilbert-Schmidt operators

  • Published:
Rendiconti del Circolo Matematico di Palermo Aims and scope Submit manuscript

Abstract

We prove that the Supercylicity Criterion for any operatorT on a Hilbert space is equivalent to the supercyclicity of the left multiplication operator induced byT in the strong operator topology.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bes and Peris A.,Hereditarily hypercyclic operators, J. Funct. Anal.,167 (1999), 94–112.

    Article  MATH  MathSciNet  Google Scholar 

  2. Chan K. C.,hypercyclicity of the operator algebra for a separable Hilbert space, J. Operator Theory,42 (1999), 231–244.

    MATH  MathSciNet  Google Scholar 

  3. Feldman N. S., Miller T. L., Miller V. G.,Hypercyclic and supercyclic cohyponormal operators, Acta. Sci. Math. (Szeged),68 (2002), 303–328.

    MATH  MathSciNet  Google Scholar 

  4. Gethner R. M., Shapiro J. H.,Universal vectors for operators on spaces of holomorphic functions, Proc. Amer. Math. Soc.,100 (1987), 281–288.

    Article  MATH  MathSciNet  Google Scholar 

  5. Godefroy G., Shapiro J. H.,Operators with dense, invariant, cyclic vector manifolds, J. Funct. Anal.,98 (1991), 229–269.

    Article  MATH  MathSciNet  Google Scholar 

  6. Hilden H. M., Wallen L. J.,Some cyclic and non-cyclic vectors of certain operators, Indiana Univ. Math. J.,24 (1974), 557–565.

    Article  MathSciNet  Google Scholar 

  7. Kitai C.,Invariant closed sets for linear operators, Ph. D. Dissertation, University of Toronto, 1982.

  8. Salas H. N.,Hypercyclic weighted shifts, Trans. Amer. Math. Soc.,347 (1995), 993–1004.

    Article  MATH  MathSciNet  Google Scholar 

  9. Salas H.,Supercyclicity and weighted shifts, Studia Math.,135 (1999), 55–74.

    MATH  MathSciNet  Google Scholar 

  10. Yousefi B., Rezaei H.,Hypercyclicity on the algebra of Hilbert-Schmidt operators, Result. Math.,46 (2004), 174–180.

    MATH  MathSciNet  Google Scholar 

  11. Yousefi B., Rezaei H.,Hypercyclic property of weighted composition operators, Proc. Amer. Math. Soc., to appear.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yousefi, B., Rezaei, H. & Doroodgar, J. Supercyclicity in the operator algebra using Hilbert-Schmidt operators. Rend. Circ. Mat. Palermo 56, 33–42 (2007). https://doi.org/10.1007/BF03031426

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03031426

AMS Subject Classification

Keyswords and phrases

Navigation