JOURNAL BROWSE
Search
Advanced SearchSearch Tips
SOME REMARKS ON THE HELTON CLASS OF AN OPERATOR
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
SOME REMARKS ON THE HELTON CLASS OF AN OPERATOR
Kim, In-Sook; Kim, Yoen-Ha; Ko, Eun-Gil; Lee, Ji-Eun;
  PDF(new window)
 Abstract
In this paper we study some properties of the Helton class of an operator. In particular, we show that the Helton class preserves the quasinilpotent property and Dunford`s boundedness condition (B). As corollaries, we get that the Helton class of some quadratically hyponormal operators or decomposable subnormal operators satisfies Dunford`s boundedness condition (B).
 Keywords
Helton class;quasinilpotent property;Dunford`s boundedness condition (B);
 Language
English
 Cited by
 References
1.
I. Colojoara and C. Foia¸s, Theory of Generalized Spectral Operators, Mathematics and its Applications, Vol. 9. Gordon and Breach, Science Publishers, New York-London-Paris, 1968

2.
J. B. Conway, A Course in Functional Analysis, Springer-Verlag, 1985

3.
S. Djordjevic, I. H. Jeon, and E. Ko, Weyl's theorem through local spectral theory, Glasg. Math. J. 44 (2002), no. 2, 323–327 crossref(new window)

4.
N. Dunford, Spectral operators, Pacific J. Math. 4 (1954), 321–354

5.
P. R. Halmos, A Hilbert Space Problem Book, Springer-Verlag, 1980

6.
R. A. Horn and C. A. Johnson, Matrix Analysis, Cambridge University Press, 1985

7.
Y. Kim, E. Ko, and J. Lee, Operators with the single valued extension property, Bull. Korean Math. Soc. 43 (2006), no. 3, 509–517 crossref(new window)

8.
K. Laursen and M. Neumann, An Introduction to Local Spectral Theory, London Mathematical Society Monographs. New Series, 20. The Clarendon Press, Oxford University Press, New York, 2000

9.
J. Lee, The Helton class of operators and rank one perturbations of the unilateral shift, Ph. D. thesis, Ewha Womans University, 2008

10.
J. G. Stampfli, Analytic extensions and spectral localization, J. Math. Mech. 16 (1966), 287–296

11.
B. L. Wadhwa, Spectral, M-hyponormal and decomposable operators, Ph. D. thesis, Indiana University, 1971