JOURNAL BROWSE
Search
Advanced SearchSearch Tips
CONTINUITY OF APPROXIMATE POINT SPECTRUM ON THE ALGEBRA B(X)
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
CONTINUITY OF APPROXIMATE POINT SPECTRUM ON THE ALGEBRA B(X)
Sanchez-Perales, Salvador; Cruz-Barriguete, Victor A.;
  PDF(new window)
 Abstract
In this paper we provide a brief introduction to the continuity of approximate point spectrum on the algebra B(X), using basic properties of Fredholm operators and the SVEP condition. Also, we give an example showing that in general it not holds that if the spectrum is continuous an operator T, then for each and > 0, the ball contains a component of , contrary to what has been announced in [J. B. Conway and B. B. Morrel, Operators that are points of spectral continuity II, Integral Equations Operator Theory 4 (1981), 459-503] page 462.
 Keywords
approximate point spectrum;continuity of the spectrum;
 Language
English
 Cited by
1.
WEYL'S THEOREM, TENSOR PRODUCT, FUGLEDE-PUTNAM THEOREM AND CONTINUITY SPECTRUM FOR k-QUASI CLASS An* OPERATO,;;

대한수학회지, 2014. vol.51. 5, pp.1089-1104 crossref(new window)
1.
WEYL'S THEOREM, TENSOR PRODUCT, FUGLEDE-PUTNAM THEOREM AND CONTINUITY SPECTRUM FOR k-QUASI CLASS An*OPERATO, Journal of the Korean Mathematical Society, 2014, 51, 5, 1089  crossref(new windwow)
 References
1.
M. Ahues, A. Largillier, and B. V. Limaye, Spectral Computations for Bounded Operators, Chapman & Hall/CRC, 2001.

2.
P. Aiena, Fredholm and Local Spectral Theory with Applications to Multipliers, Kluwer Acad., 2004.

3.
C. Apostol, L. A. Fialkow, D. A. Herrero, and D. Voiculescu, Approximation of Hilbert space operators. Vol. II, Res. Notes Math. 102, Pitman, Boston, 1984.

4.
L. Burlando, Continuity of spectrum and spectral radius in algebras of operators, Ann. Fac. Sci. Toulouse Math. 9 (1988), no. 1, 5-54. crossref(new window)

5.
S. R. Caradus, W. E. Pfaffenberger, and B. Yood, Calkin Algebras and Algebras of Operators on Banach Spaces, Marcel Dekker, 1974.

6.
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)

7.
J. B. Conway and B. B. Morrel, Operators that are points of spectral continuity. II, Integral Equations Operator Theory 4 (1981), no. 4, 459-503. crossref(new window)

8.
S. V. Djordjevic, The continuity of the essential approximative point spectrum, Facta Univ. Ser. Math. Inform. 10 (1995), 97-104.

9.
S. V. Djordjevic and Y. M. Han, Browder's theorems and spectral continuity, Glasg. Math. J. 42 (2000), no. 3, 479-486. crossref(new window)

10.
S. V. Djordjevic and Y. M. Han, Operator matrices and spectral continuity, Glasg. Math. J. 43 (2001), no. 3, 487-490.

11.
B. P. Duggal, I. H. Jeon, and I. H. Kim, Continuity of the spectrum on a class of upper triangular operator matrices, J. Math. Anal. Appl. 370 (2010), 584-587. crossref(new window)

12.
P. R. Halmos and G. Lumer, Square roots of operators. II, Proc. Amer. Math. Soc. 5 (1954), 589-595. crossref(new window)

13.
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)

14.
J. D. Newburgh, The variation of Spectra, Duke Math. J. 18 (1951), 165-176. crossref(new window)

15.
S. Sanchez-Perales and S. V. Djordjevic, Continuity of spectrum and approximate point spectrum on operator matrices, J. Math. Anal. Appl. 378 (2011), no. 1, 289-294. crossref(new window)