Abstract: In this paper,We mainly discuss some subclasses of analytic functions for operators on H, and determine a representation formula and sufficient condition for the class Φ_p^*(α,β,γ,ε,η) and prove a sufficient and necessary condition.coefficient estimates and distortiontheorem for the subclass Φ_p0^*(α,β,γ,ε,η) of the class Φ_p^*(α,β,γ,ε,η).Furthermore,the analogues also are true for operators on Hilbert space.