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SOME RESULTS ON GENERALIZED TOEPLITZ OPERATOR ON GENERALIZED HARDY SPACE

Year 2016, Volume: 6 Issue: 2, 185 - 192, 01.12.2016

Abstract

In this paper, we de ne and study some properties of the generalized Hardy space HF;2; where F is an injective linear transform from Lp  into Lp  and  is the unit circle in the complex plane C: Also we introduce the concept of a generalized Toeplitz operator on HF;2 and prove some of its properties. Further results are presented.

References

  • Abrahamse,M.B., (1971), Toeplitz operators in multiply connected regions, Bull. Amer. Math. Soc., Vol. 771971, pp. 449-454.
  • Diestel,J. and Uhl,J.R., (1977), Vector Measures, Amer. Math. Soc. Math. Surveys, Vol. 15.
  • Douglas,R.G., (1972), Banach Algebra Techniques in Operator Theory. Academic Press.
  • Faour,N.S., (1982), Toeplitz operators on Bergmann and Hardy spaces, Houston J. Math., Vol. 18, pp. 185-191.
  • Fatehi,M., (2010), On the generalized Hardy spaces, Abs. and appl. anal., Vol. 2010, pp. 1-14.
  • Rabindranathan,M., (1969), On the inversion of Toeplitz operators, J. Math. Mech., Vol. 19.
  • Rochberg,R., (1977), Toeplitz operators on weighted Hpspaces, Indiana Univ. Math. J., Vol. 26, pp. 291-298.
  • Vukoti´c,D., (2003), Analytic Toeplitz operators on the Hardy space Hp: A Survey, Bull. Belg. Math. Soc., Vol.10, pp. 101-113.
  • Wermer,J., (1976), Banach Algebras and Several Complex Variables, Springer-Verlag.
  • Widom,H., (1966), Toeplitz operators on Hp, Pacific J. Math., Vol. 19, pp. 573-582.
  • Sharifa Al-Sharif, for the photograph and short biography, see TWMS J. Appl. and Eng. Math., V.4, No.2, 2014.
Year 2016, Volume: 6 Issue: 2, 185 - 192, 01.12.2016

Abstract

References

  • Abrahamse,M.B., (1971), Toeplitz operators in multiply connected regions, Bull. Amer. Math. Soc., Vol. 771971, pp. 449-454.
  • Diestel,J. and Uhl,J.R., (1977), Vector Measures, Amer. Math. Soc. Math. Surveys, Vol. 15.
  • Douglas,R.G., (1972), Banach Algebra Techniques in Operator Theory. Academic Press.
  • Faour,N.S., (1982), Toeplitz operators on Bergmann and Hardy spaces, Houston J. Math., Vol. 18, pp. 185-191.
  • Fatehi,M., (2010), On the generalized Hardy spaces, Abs. and appl. anal., Vol. 2010, pp. 1-14.
  • Rabindranathan,M., (1969), On the inversion of Toeplitz operators, J. Math. Mech., Vol. 19.
  • Rochberg,R., (1977), Toeplitz operators on weighted Hpspaces, Indiana Univ. Math. J., Vol. 26, pp. 291-298.
  • Vukoti´c,D., (2003), Analytic Toeplitz operators on the Hardy space Hp: A Survey, Bull. Belg. Math. Soc., Vol.10, pp. 101-113.
  • Wermer,J., (1976), Banach Algebras and Several Complex Variables, Springer-Verlag.
  • Widom,H., (1966), Toeplitz operators on Hp, Pacific J. Math., Vol. 19, pp. 573-582.
  • Sharifa Al-Sharif, for the photograph and short biography, see TWMS J. Appl. and Eng. Math., V.4, No.2, 2014.
There are 11 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Sh. Al-sharif This is me

Y. Jebreel This is me

A. Khanfer This is me

Publication Date December 1, 2016
Published in Issue Year 2016 Volume: 6 Issue: 2

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