DOI QR코드

DOI QR Code

ON PREHERMITIAN OPERATORS

  • YOO JONG-KWANG (Department of Liberal Arts and Science Chodang University) ;
  • HAN HYUK (Department of Mathematics Seonam University)
  • Published : 2006.01.01

Abstract

In this paper, we are concerned with the algebraic representation of the quasi-nilpotent part for prehermitian operators on Banach spaces. The quasi-nilpotent part of an operator plays a significant role in the spectral theory and Fredholm theory of operators on Banach spaces. Properties of the quasi-nilpotent part are investigated and an application is given to totally paranormal and prehermitian operators.

Keywords

References

  1. P. Aiena, T. L. Miller and M. M. Neumann, On a localized single-valued exten- sion property, Preprint, Mississippi State University (2001)
  2. E. Albrecht, Funktionalkalkule in mehreren Verranderlichen fur stetige lineare Operatoren auf Banachraumen, Manuscripta Math. 14 (1974), 1-40 https://doi.org/10.1007/BF01637620
  3. C. Apostol, Spectral decompositions and functional calculus, Rev. Roum. Math. Pures et Appl. 13 (1968), 1481-1528
  4. K. Clancey, Seminormal operators, Lecture Notes in Math., vol. 742, Springer, New York, 1979
  5. I. Colojoara and C. Foias, Theory of generalized spectral operators, Gorden and Breach, New York, 1968
  6. H. R. Dowson, Spectral Theory of linear operators, Academic Press, New York, 1978
  7. K. B. Laursen and M. M. Neumann, Asymptotic intertwining and spectral inclusions on Banach spaces, Czech. Math. J. 43(118) (1993), 483-497
  8. K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, London Mathematical Society Monographs New Series 20, Oxford Science Publications, Oxford, 2000
  9. G. Lumer, Spectral operators, hermitians operators, and bounded groups, Acta Sci. Math. 25 (1964), 75-85
  10. M. Mbekhta, Sur la theorie spectrale locale et limite des nilpotents, Proc. Amer. Math. Soc. 112 (1991), 621-631
  11. T. L. Miller and V. G. Miller, Equality of essential spectra of quasisimilar op- erators with property ($\delta$), Glasgow Math. J. 38 (1996), 21-28 https://doi.org/10.1017/S0017089500031219
  12. P. Vrbova, On local spectral properties of operators in Banach spaces, Czech. Math. J. 23(98) (1973), 483-492
  13. P. Vrbova, Structure of maximal spectral spaces of generalized scalar operators, Czech. Math. J. 23 (1973), 493-496
  14. J. K. Yoo, Admissible operators, Far East J. Math. Sci. 8 (2003), no. 2, 223-234