JOURNAL BROWSE
Search
Advanced SearchSearch Tips
THE SPECTRAL CONTINUITY OF ESSENTIALLY HYPONORMAL OPERATORS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
THE SPECTRAL CONTINUITY OF ESSENTIALLY HYPONORMAL OPERATORS
Kim, An-Hyun; Ryu, Eun-Jin;
  PDF(new window)
 Abstract
If A is a unital Banach algebra, then the spectrum can be viewed as a function : 𝕬 𝕾, mapping each T 𝕬 to its spectrum , where 𝕾 is the set, equipped with the Hausdorff metric, of all compact subsets of . This paper is concerned with the continuity of the spectrum via Browder's theorem. It is shown that is continuous when is restricted to the set of essentially hyponormal operators for which Browder's theorem holds, that is, the Weyl spectrum and the Browder spectrum coincide.
 Keywords
spectrum;essential spectrum;spectral continuity;Weyl's theorem;Browder's theorem;
 Language
English
 Cited by
 References
1.
S. K. Berberian, An extension of Weyl's theorem to a class of not necessarily normal operators, Michigan Math. J. 16 (1969), 273-279. crossref(new window)

2.
R. H. Bouldin, The essential minimum modulus, Indiana Univ. Math. J. 30 (1981), no. 4, 513-517. crossref(new window)

3.
R. H. Bouldin, Distance to invertible linear operators without separability, Proc. Amer. Math. Soc. 116 (1992), no. 2, 489-497. crossref(new window)

4.
A. Bottcher, S. Grudsky, and I. Spitkovsky, The spectrum is discontinuous on the manifold of Toeplitz operators, Arch. Math. 75 (2000), no. 1, 46-52. crossref(new window)

5.
A. Bottcher and B. Silbermann, Analysis of Toeplitz Operators, Springer, Berlin-Heidelberg-New York, 1990.

6.
L. A. Coburn, Weyl's theorem for nonnormal operators, Michigan Math. J. 13 (1966), 285-288. crossref(new window)

7.
J. B. Conway and B. B. Morrel, Operators that are points of spectral continuity, Integral Equations Operator Theory 2 (1979), no. 2, 174-198. crossref(new window)

8.
R. G. Douglas, Banach Algebra Techniques in Operator Theory, Academic press, New York, 1972.

9.
D. R. Farenick and W. Y. Lee, Hyponormality and spectra of Toeplitz operators, Trans. Amer. Math. Soc. 348 (1996), no. 10, 4153-4174. crossref(new window)

10.
P. R. Halmos, A Hilbert Space Problem Book, Springer, New York, 1982.

11.
R. E. Harte, Invertibility and Singularity for Bounded Linear Operators, Dekker, New York, 1988.

12.
R. E. Harte and W. Y. Lee, Another note on Weyl's theorem, Trans. Amer. Math. Soc. 349 (1997), no. 5, 2115-2124. crossref(new window)

13.
D. A. Herrero, Economical compact perturbations I: Erasing normal eigenvalues, J. Operator Theory 10 (1983), no. 2, 289-306.

14.
I. S. Hwang and W. Y. Lee, On the continuity of spectra of Toeplitz operators, Arch. Math. 70 (1998), no. 1, 66-73. crossref(new window)

15.
I. S. Hwang and W. Y. Lee, The spectrum is continuous on the set of p-hyponormal operators, Math. Z. 235 (2000), no. 1, 151-157. crossref(new window)

16.
A. H. Kim and E. Y. Kwon, Spectral continuity of essentially p-hyponormal operators, Bull. Korean Math. Soc. 43 (2006), no. 2, 389-393. crossref(new window)

17.
J. D. Newburgh, The variation of spectra, Duke Math. J. 18 (1951), 165-176. crossref(new window)

18.
N. K. Nikolskii, Treatise on the Shift Operator, Springer, New York, 1986.

19.
C. M. Pearcy, Some Recent Developments in Operator Theory, CBMS 36, Providence: AMS, 1978.

20.
H. Weyl, Uber beschrankte quadratische Formen, deren Differenz vollsteig ist, Rend. Circ. Mat. Palermo 27(1909), 373-392. crossref(new window)

21.
H. Widom, On the spectrum of a Toeplitz operator, Pacific J. Math. 14 (1964), 365-375. crossref(new window)