摘要
In this paper,we study mainly properties of a class approx mate ope rator in Hilbert space, form as S=T+Q where T is a power class (N) operator and Q is a quasinilpotent opera tot with TQ=QT. We discuss relation of kernel of operator S and T and Q, while discuss properties of its spectrum by using the ultraproduct theory and prove that for a bounded sequence of point {x_n} in H,Sx_n→O iff Tx_n→O and Qx_n→O.
