Stability of Admissible Functions

By using the concept of the weak subordination, we examine the stability (a class of analytic functions in the unit disk is said to be stable if it is closed under weak subordination) for a class of admissible functions in complex Banach spaces. The stabilityof analytic functions in the following classes is discussed: Bloch class, little Bloch class,hyperbolic little Bloch class, extend Bloch class (Qp), and Hilbert Hardy class (H2)