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

Studia Mathematica (2000)

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

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topDjordjević, 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

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