On Composition Operators on A2

If (?) is an analytic function mapping the open unit disk D into itself and A2 is the Bergman space of analytic functions on D, the compositon operator C?, on A2 is defined by C?f=fo?feA2. In this paper we consider the spectral radius, unitary equivalence, sub-normality of C? and study the case ?(z) = zm, m = 2, 3,….. in detail.