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SPECTRAL CONTINUITY OF ESSENTIALLY p-HYPONORMAL OPERATORS

  • Kim, An-Hyun (DEPARTMENT OF MATHEMATICS, CHANGWON NATIONAL UNIVERSITY) ;
  • Kwon, Eun-Young (DEPARTMENT OF MATHEMATICS, CHANGWON NATIONAL UNIVERSITY)
  • Published : 2006.05.01

Abstract

In this paper it is shown that the spectrum ${\sigma}$ is continuous at every p-hyponormal operator when restricted to the set of essentially p-hyponormal operators and moreover ${\sigma}$ is continuous when restricted to the set of compact perturbations of p-hyponormal operators whose spectral pictures have no holes associated with the index zero.

Keywords

References

  1. A. Aluthge, On p-hyponormal operators for 0 < p < 1, Integral Equations Operator Theory 13 (1990), no. 3, 307-315 https://doi.org/10.1007/BF01199886
  2. M. Cho and T. Huruya, p{hyponormal operators for 0 < p < $\frac{1}{2}$, Comment. Math. Prace Mat. 33 (1993), 23-29
  3. M. Cho, M. Itoh, and S. Oshiro, Weyl's theorem holds for p-hyponormal oper- ators, Glasgow Math. J. 39 (1997), no. 2, 217-220 https://doi.org/10.1017/S0017089500032092
  4. J. B. Conway and B. B. Morrel, Operators that are points of spectral continuity, Integral Equations Operator Theory 2 (1979), no. 2, 174-198 https://doi.org/10.1007/BF01682733
  5. D. R. Farenick and W. Y. Lee, Hyponormality and spectra of Toeplitz operators, Trans. Amer. Math. Soc. 348 (1996), no. 10, 4153-4174 https://doi.org/10.1090/S0002-9947-96-01683-2
  6. J. K. Finch, The single valued extension property on a Banach space, Pacific J. Math. 58 (1975), no. 1, 61-69 https://doi.org/10.2140/pjm.1975.58.61
  7. P. R. Halmos, A Hilbert Space Problem Book, Springer, New York, 1982
  8. R. E. Harte, Invertibility and Singularity for Bounded Linear Operators, Marcel Dekker, Inc., New York, 1988
  9. I. S. Hwang and W. Y. Lee, On the continuity of spectra of Toeplitz operators, Arch. Math. (Basel) 70 (1998), no. 1, 66-73 https://doi.org/10.1007/s000130050166
  10. I. S. Hwang and W. Y. Lee, The spectrum is continuous on the set of p-hyponormal operators, Math. Z. 235 (2000), no. 1, 151-157 https://doi.org/10.1007/s002090000128
  11. K. B. Laursen, Operators with finite ascent, Pacific J. Math. 152 (1992), no. 2, 323-336 https://doi.org/10.2140/pjm.1992.152.323
  12. J. D. Newburgh, The variation of spectra, Duke Math. J. 18 (1951), 165-176 https://doi.org/10.1215/S0012-7094-51-01813-3

Cited by

  1. THE SPECTRAL CONTINUITY OF ESSENTIALLY HYPONORMAL OPERATORS vol.29, pp.3, 2014, https://doi.org/10.4134/CKMS.2014.29.3.401