Weyl's theorems and continuity of spectra in the class of p-hyponormal operators

S. Djordjević; B. Duggal

Studia Mathematica (2000)

  • Volume: 143, Issue: 1, page 23-32
  • ISSN: 0039-3223

Abstract

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We show that p-hyponormal operators obey Weyl's and a-Weyl's theorem. Also, we show that the spectrum, Weyl spectrum, Browder spectrum and approximate point spectrum are continuous functions in the class of all p-hyponormal operators.

How to cite

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Djordjević, S., and Duggal, B.. "Weyl's theorems and continuity of spectra in the class of p-hyponormal operators." Studia Mathematica 143.1 (2000): 23-32. <http://eudml.org/doc/216807>.

@article{Djordjević2000,
abstract = {We show that p-hyponormal operators obey Weyl's and a-Weyl's theorem. Also, we show that the spectrum, Weyl spectrum, Browder spectrum and approximate point spectrum are continuous functions in the class of all p-hyponormal operators.},
author = {Djordjević, S., Duggal, B.},
journal = {Studia Mathematica},
keywords = {p-hyponormal operators; Weyl's theorem; continuity of spectra; hyponormal operators; spectrum; Weyl spectrum; Browder spectrum; approximate point spectrum},
language = {eng},
number = {1},
pages = {23-32},
title = {Weyl's theorems and continuity of spectra in the class of p-hyponormal operators},
url = {http://eudml.org/doc/216807},
volume = {143},
year = {2000},
}

TY - JOUR
AU - Djordjević, S.
AU - Duggal, B.
TI - Weyl's theorems and continuity of spectra in the class of p-hyponormal operators
JO - Studia Mathematica
PY - 2000
VL - 143
IS - 1
SP - 23
EP - 32
AB - We show that p-hyponormal operators obey Weyl's and a-Weyl's theorem. Also, we show that the spectrum, Weyl spectrum, Browder spectrum and approximate point spectrum are continuous functions in the class of all p-hyponormal operators.
LA - eng
KW - p-hyponormal operators; Weyl's theorem; continuity of spectra; hyponormal operators; spectrum; Weyl spectrum; Browder spectrum; approximate point spectrum
UR - http://eudml.org/doc/216807
ER -

References

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  1. [1] A. Aluthge, On p-hyponormal operators for 0 < p < 1, Integral Equations Operator Theory 13 (1990), 307-315. 
  2. [2] J. V. Baxley, On the Weyl spectrum of a Hilbert space operator, Proc. Amer. Math. Soc. 34 (1972), 447-452. Zbl0256.47001
  3. [3] S. K. Berberian, Approximate proper vectors, ibid. 13 (1962), 111-114. Zbl0166.40503
  4. [4] M. Chō and A. Huruya, p-hyponormal operators for 0 < p < 1/2, Comment. Math. 33 (1993), 23-29. 
  5. [5] M. Chō, M. Itoh and S. Ōshiro, Weyl's theorem holds for p-hyponormal operators, Glasgow Math. J. 39 (1997), 217-220. 
  6. [6] S. V. Djordjević, On continuity of the essential approximate point spectrum, Facta Univer. (Niš) 10 (1995), 97-104. Zbl0889.47009
  7. [7] S. V. Djordjević and D. S. Djordjević, Weyl's theorems: continuity of the spectrum and quasihyponormal operators, Acta Sci. Math. (Szeged) 64 (1998), 259-269. Zbl0918.47014
  8. [8] B. P. Duggal, On quasi-similar p-hyponormal operators, Integral Equations Operator Theory 26 (1996), 338-345. Zbl0866.47014
  9. [9] S. Kurepa, Funkcionalna analiza, Školska knjiga, Zagreb, 1981 (in Croatian). 
  10. [10] J. D. Newburgh, The variation of spectra, Duke Math. J. 18 (1951), 165-176. Zbl0042.12302
  11. [11] V. Rakočević, On the essential approximate point spectrum II, Mat. Vesnik 36 (1984), 89-97. Zbl0535.47002
  12. [12] V. Rakočević, Operators obeying a-Weyl's theorem, Rev. Roumaine Math. Pures Appl. 34 (1989), 915-919. Zbl0686.47005
  13. [13] M. Schechter, Principles of Functional Analysis, 2nd printing, Academic Press, New York, 1973. 
  14. [14] A. Uchiyama, Berger-Shaw's theorem for p-hyponormal operators, Integral Equations Operator Theory 33 (1999), 221-230. Zbl0924.47015

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