Commun. Korean Math. Soc. 2006 Vol. 21, No. 1, 53-64 Printed March 1, 2006
Jong-Kwang Yoo, Hyuk Han Chodang University, Seonam University
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
