# ON PREHERMITIAN OPERATORS

• Published : 2006.01.01
• 60 11

#### 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

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