Some results on polynomially Drazin normal operators
Abstract
For T ∈ B_d (H) (the set of Drazin invertible operators), we say that T is polynomially Drazin normal if there exits a non trivial complex polynomial P such that
P(T^D)T * − T* P(T^ D) = 0, or equivalently, 0≤k≤n In this paper we study some structural properties of polynomially Drazin normal operators.
Our motivation for this study comes from the problem of finding operators that their Drazin inverses are polynomially normal operators.
Keywords
Hilbert space, $n$-normal, $(n,m)$-normal, Polynomially normal, Drazin inverse