ON PREHERMITIAN OPERATORS

Title & Authors
ON PREHERMITIAN OPERATORS
YOO JONG-KWANG; HAN HYUK;

Abstract
In this paper, we are concerned with the algebraic representation of the quasi-nilpotent part for prehermitian operators on Banach spaces. The quasi-nilpotent part of an operator plays a significant role in the spectral theory and Fredholm theory of operators on Banach spaces. Properties of the quasi-nilpotent part are investigated and an application is given to totally paranormal and prehermitian operators.
Keywords
algebraic spectral subspace;analytic spectral subspace;local spectral radius;normal-equivalent and prehermitian operator;
Language
English
Cited by
References
1.
P. Aiena, T. L. Miller and M. M. Neumann, On a localized single-valued exten- sion property, Preprint, Mississippi State University (2001)

2.
E. Albrecht, Funktionalkalkule in mehreren Verranderlichen fur stetige lineare Operatoren auf Banachraumen, Manuscripta Math. 14 (1974), 1-40

3.
C. Apostol, Spectral decompositions and functional calculus, Rev. Roum. Math. Pures et Appl. 13 (1968), 1481-1528

4.
K. Clancey, Seminormal operators, Lecture Notes in Math., vol. 742, Springer, New York, 1979

5.
I. Colojoara and C. Foias, Theory of generalized spectral operators, Gorden and Breach, New York, 1968

6.
H. R. Dowson, Spectral Theory of linear operators, Academic Press, New York, 1978

7.
K. B. Laursen and M. M. Neumann, Asymptotic intertwining and spectral inclusions on Banach spaces, Czech. Math. J. 43(118) (1993), 483-497

8.
K. B. Laursen and M. M. Neumann, An Introduction to Local Spectral Theory, London Mathematical Society Monographs New Series 20, Oxford Science Publications, Oxford, 2000

9.
G. Lumer, Spectral operators, hermitians operators, and bounded groups, Acta Sci. Math. 25 (1964), 75-85

10.
M. Mbekhta, Sur la theorie spectrale locale et limite des nilpotents, Proc. Amer. Math. Soc. 112 (1991), 621-631

11.
T. L. Miller and V. G. Miller, Equality of essential spectra of quasisimilar op- erators with property ($\delta$), Glasgow Math. J. 38 (1996), 21-28

12.
P. Vrbova, On local spectral properties of operators in Banach spaces, Czech. Math. J. 23(98) (1973), 483-492

13.
P. Vrbova, Structure of maximal spectral spaces of generalized scalar operators, Czech. Math. J. 23 (1973), 493-496

14.
J. K. Yoo, Admissible operators, Far East J. Math. Sci. 8 (2003), no. 2, 223-234