Ilmi Hoxha and Naim

In this paper, we introduce a new class of operators, called k−quasi class An operators, which is a superclass of hyponormal operators and a subclass of (n, k)−quasi−∗−paranormal operators. We will show basic structural properties and some spectral properties of this class of operators. We show that, if T ∈ An then σjp(T ) = σp(T ), σja(T ) = σa(T ) and T − λ has finite ascent for all λ ∈ C. Also, we will prove Browder’s theorem, a−Browders theorem for k−quasi class An operator.