On reflexivity, denseness and compactness of numerical radius attainable operators

  • Sabasi Omaoro Department of mathematics, Kisii University, Box 408-40200, Kisii
  • J. Kerongo Department of mathematics, Kisii University, Box 408-40200, Kisii
  • R. K. Obogi Department of mathematics, Kisii University, Box 408-40200, Kisii
  • N. B. Okelo Department of Pure and Applied mathematics, Jaramogi Oginga Odinga of Science and Technology, Box 210-40601, Bondo
Keywords: Reflexivity, Compactness, Denseness, Numerical radius attainability, Normal operators and Self-adjoint operators

Abstract

In this paper, we study the properties of normal self-adjoint operators. We concentrate on some of their properties, for example, reflexivity, denseness and compactness. We also give some results on norm-attainability.

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References

Acosta M. D., Agurre F. J., Paya R., A space by W. Gowers and new results on norm and numerical radius attaining operators. Acta universitatis Caroline. Math. Et physica., Vol.33, no.2, (1992), 5-14.

Acosta M. D., Galan M. R., Reflexivity spaces and numerical radius attaining operators. J. Extracta math., Vol.15, no.2, (2000), 247-255.

Acosta M. D., Paya R., Numerical radius attaining operators. Extracta math. Vol.2, (1987), 74-76.

Bishop, E., Phelps, R. R., A proof that every Banach space is sub reflexive. Bull. Amer. Math. Soc., Vol.67, (1961), 97-98.

Chi-kwong L., Lecture notes on numerical Ranges. Department of math. College of William and Mary, Virginia 23187-8795. (2005).

Gowers W., Symmetric block bases of sequences with large average growth. J. Israel j. Math., Vol.169, (1990), 129-149.

Gustafson K.E., et al, Numerical Range. Springer-verlay, New York, inc., (1997).

Honke D., Wang Y., Jianming L. Reduced minimal numerical ranges of operators on a Hilbert space. J. Acta math. Scientia., Vol.29B, no.1, (2009), 94-100.

Joachim w., Linear operators in Hilbert spaces. Spring-Verlag, New York, (1980).

Omidvar M. E., Moslehian M. S., Niknam A. Some numerical radius inequalities for Hilbert space operators., Involve 2.4, (2009), 471-478.

Shapiro J. H., Notes on the numerical range. Michigan state University, East Lansing,MI 48824-1027, USA.

Yul E., Vitali M., Antonis T., Functional Analysis: An introduction. American Mathematical Society, New York, (2004).

Kittaneh F., Numerical radius inequality and an estimate for numerical radius of the Frobenius companion matrix. Studia math., Vol.158, no.1, (2003), 11-17.

Published
2015-05-25
How to Cite
Omaoro, S., Kerongo, J., Obogi, R., & Okelo, N. (2015). On reflexivity, denseness and compactness of numerical radius attainable operators. Bulletin of Advanced Scientific Research, 1(1), 10-11. Retrieved from http://asdpub.com/index.php/basr/article/view/89
Section
Original Articles

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