Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
권호 표지
DOI QR코드

DOI QR Code

A NOTE ON SPECTRAL CONTINUITY

  • JEON, IN HO (Department of Mathematics Education Seoul National University of Education) ;
  • KIM, IN HYOUN (Department of Mathematics Incheon National University)
  • Received : 2015.10.15
  • Accepted : 2015.09.18
  • Published : 2015.12.30
Download PDF
⟨ Previous Next ⟩

Abstract

In the present note, provided $T{\in}{\mathfrak{L}}({\mathfrak{H}})$ is biquasitriangular and Browder's theorem hold for T, we show that the spectrum ${\sigma}$ is continuous at T if and only if the essential spectrum ${\sigma}_e$ is continuous at T.

Keywords

References

  1. C. Apostol, C. Foias and D. Voiculescu, Some results on non-quasitriangular operators. IV, Rev. Roum. Math. Pures Appl. 18 (1973), 487-514.
  2. J. B. Conway and B. B. Morrel, Operators that are points of spectral continuity, Integral equations and operator theory, 2 (1979), 174-198. https://doi.org/10.1007/BF01682733
  3. J. B. Conway and B. B. Morrel, Operators that are points of spectral continuity II, Integral equations and operator theory 4 (1981), 459-503. https://doi.org/10.1007/BF01686497
  4. N. Dunford, Spectral operators, Pacific J. Math. 4 (1954), 321-354. https://doi.org/10.2140/pjm.1954.4.321
  5. S. V. Djordjevic and B. P. Duggal, Weyl's theorem and continuity of spectra in the class of p-hyponormal operators, Studia Math. 143 (2000), 23-32. https://doi.org/10.4064/sm-143-1-23-32
  6. S. V.Djordjevic and Y. M. Han, Browder's theorem and spectral continuity, Glasgow Math. J. 42 (2000), 479-486. https://doi.org/10.1017/S0017089500030147
  7. S. V.Djordjevic, Continuity of the essential spectrum in the class of quasihy-ponormal operators, Vesnik Math. 50 (1998) 71-74.
  8. B. P. Duggal, I. H. Jeon, and I. H. Kim, Continuity of the spectrum on a class of upper triangular operator matrices, Jour. Math. Anal. Appl. 370 (2010), 584-587. https://doi.org/10.1016/j.jmaa.2010.04.068
  9. R. Harte and W. Y. Lee, Another note on Weyl's theorem, Trans. Amer. Math. Soc. 349 (1997), 2115-2124. https://doi.org/10.1090/S0002-9947-97-01881-3
  10. I. S. Hwang and W. Y. Lee, The spectrum is continuous on the set of p-hyponormal operators, Math. Z. 235 (2000), 151-157. https://doi.org/10.1007/s002090000128
  11. R. Lange, Biquasitriangularity and spectral continuity, Glasgow Math. J. 26 (1985), 177-180. https://doi.org/10.1017/S0017089500005966
  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