DOI QR코드

DOI QR Code

ON THE SPECTRAL CONTINUITY

  • Lee, Jae Won (Department of Applied Mathematics Kumoh National Institute of Technology) ;
  • Jeon, In Ho (Department of Mathematics Education Seoul National University of Education)
  • Received : 2015.02.27
  • Accepted : 2015.03.06
  • Published : 2015.03.30

Abstract

In this paper we show that the spectrum is continuous on the class of ${\star}$-paranormal operators but the approximate point spectrum generally is not continuous at ${\star}$-paranormal operators.

Keywords

Acknowledgement

Supported by : Kumoh National Institute of Technology

References

  1. P. Aiena, Operators which have a closed quasi-nilpotent part, Proc. Amer. Math. soc. 130 (2002), 2701-2710. https://doi.org/10.1090/S0002-9939-02-06386-4
  2. C. Apostol, C. Foias and D. Voiculescu, Some results on non-quasitriangular operators. IV, Rev. Roum. Math. Pures Appl. 18 (1973), 487-514.
  3. S. K. Berberian Approximate proper vectors, Proc. Amer. Math. Soc. 13 (1962), 111-114. https://doi.org/10.1090/S0002-9939-1962-0133690-8
  4. 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
  5. 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
  6. N. Dunford, Spectral operators, Pacific J. Math. 4 (1954), 321-354. https://doi.org/10.2140/pjm.1954.4.321
  7. 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
  8. S. V.Djordjevic, Continuity of the essential spectrum in the class of quasihyponormal operators, Vesnik Math. 50 (1998), 71-74.
  9. 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
  10. B. P. Duggal, I. H. Jeon, and I. H. Kim, On *-paranormal contractions and properties for *-class A operators, Linear Algebra Appl. 436 (2012), 954-962. https://doi.org/10.1016/j.laa.2011.06.002
  11. P. B. Halmos, A Hilbert Space Problem Book, Van Nostrand, Princeton 1967.
  12. 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
  13. T. Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Anal. Math. 6 (1958), 261-322. https://doi.org/10.1007/BF02790238
  14. J. W. Lee and I. H. Jeon, Continuity of the spectrum on (classA)*, Korean J. Math. 21 (2013), 35-39. https://doi.org/10.11568/kjm.2013.21.1.35
  15. M. Mbekhta, Generalisation de la decomposition de Kato aux operateurs paranormaux et spectraux, Glasgow Math. J. 29 (1987), 159-175. https://doi.org/10.1017/S0017089500006807
  16. J. D. Newburgh, The variation of spectra, Duke Math. J. 18 (1951), 165-176. https://doi.org/10.1215/S0012-7094-51-01813-3
  17. M. Oudghiri, Weyl's and Browder's theorem for operators satisfying the SVEP, Studia Math. 163 (2004), 85-101. https://doi.org/10.4064/sm163-1-5