Korean J. Math. Vol. 23 No. 1 (2015) pp.65-72
DOI: https://doi.org/10.11568/kjm.2015.23.1.65

On the spectral continuity

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Published: Mar 30, 2015
Keywords:
spectral continuity, single valued extension property, Kato's type, quasitriangular, $\star$-paranormal
Mathematics Subject Classification:
47A10, 47A53, 47B20

Main Article Content

Jae Won Lee
Department of Applied Mathematics Kumoh National Institute of Technology Gumi 730-70, Korea
In Ho Jeon
Department of Mathematics Education Seoul National University of Education Seoul 137-742, Korea

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.


Article Details

Supporting Agencies

This paper was supported by Research Fund 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. Google Scholar

[2] C. Apostol, C. Foias and D. Voiculescu, Some results on non-quasitriangular operators. IV, Rev. Roum. Math. Pures Appl. 18 (1973), 487–514. Google Scholar

[3] S. K. Berberian Approximate proper vectors, Proc. Amer. Math. Soc. 13 (1962), 111–114. Google Scholar

[4] J. B. Conway and B. B. Morrel, Operators that are points of spectral continuity, Integral equations and operator theory, 2 (1979), 174-198. Google Scholar

[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. Google Scholar

[6] N. Dunford, Spectral operators, Pacific J. Math. 4 (1954), 321–354. Google Scholar

[7] S. V. Djordjevi c and B. P. Duggal, Weyl's theorem and continuity of spectra in the class of p-hyponormal operators, Studia Math. 143 (2000), 23-32. Google Scholar

[8] S. V.Djordjevi c, Continuity of the essential spectrum in the class of quasihy-ponormal operators, Vesnik Math. 50 (1998), 71-74. Google Scholar

[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. Google Scholar

[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. Google Scholar

[11] P. B. Halmos, A Hilbert Space Problem Book, Van Nostrand, Princeton 1967. Google Scholar

[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. Google Scholar

[13] T. Kato, Perturbation theory for nullity, deficiency and other quantities of linear operators, J. Anal. Math. 6 (1958), 261–322. Google Scholar

[14] J. W. Lee and I. H. Jeon, Continuity of the spectrum on (classA)∗, Korean J. Math. 21 (2013), 35-39. Google Scholar

[15] M. Mbekhta, G en eralisation de la d ecomposition de Kato aux op erateurs para- normaux et spectraux, Glasgow Math. J. 29 (1987), 159-175. Google Scholar

[16] J. D. Newburgh, The variation of spectra, Duke Math. J. 18 (1951), 165–176. Google Scholar

[17] M. Oudghiri, Weyl’s and Browder’s theorem for operators satisfying the SVEP, Studia Math. 163 (2004), 85–101. Google Scholar