The essential norm of a composition operator on Orlicz spaces

In this note we determine the lower and upper estimates for the essential norm of a composition operator on the Orlicz spaces under certain conditions.

The essential norm of a composition operator on Orlicz spaces

In this note we determine the lower and upper estimates for the essential norm of a composition operator on the Orlicz spaces under certain conditions.

___

  • Cui, Y., Hudzik, H., Kumar, R. and Maligranda, L.: Composition operators in Orlicz spaces, J. Aust. Math. Soc. 76, 189-206 (2004).
  • Jabbarzadeh, M. R.: A note on weighted composition operators on measurable function spaces, J. Korean Math. Soc. 41, 95-105 (2004).
  • Komal, B. S. and Gupta, Shally: Composition operators on Orlicz spaces, Indian J. Pure Appl. Math. 32, 1117-1122 (2001).
  • Kufner, A., John, O. and Fuc˘ik, S.: Function spaces, Academia Prague, 1977.
  • Kumar, R.: Composition operators on Orlicz spaces, Integral Equations Operator Theory 29, 17-22 (1997).
  • Montes-Rodr´ıguez, A.: The essential norm of a composition operator on Bloch spaces, PaciŞc J. Math. 188, 339-351 (1999).
  • Rao, M. M. and Ren, Z. D.: Theory of Orlicz spaces, Marcel Dekker, Inc. New York, 1991.
  • Shapiro, J. H.: The essential norm of a composition operator, Analls of Math. 125, 375-404 (1987).
  • Takagi, T., Miura, T. and Takahasi, Sin-Ei: Essential norm and stability constants of weighted composition operators on C(X) , Bull. Korean Math. Soc. 40, 583-591 (2003).
  • Zaanen, A. C.: Integration, 2nd ed., North-Holland, Amsterdam, 1967.
  • Zheng, L.: The essential norms and spectra of composition operators on H∞, PaciŞc J. Math. 203, 503-510 (2002). M. R. JABBARZADEH
  • Faculty of Mathematical Sciences,
  • University of Tabriz, P. O. Box: 51664, Tabriz-IRAN
  • e-mail: mjabbar@tabrizu.ac.ir