Duality of the nonreflexive Bergman space of the upper half plane and Composition groups

We identify the predual of the nonreflexive Bergman space of the upper half plane, $L_a^1(\text{uP},{\mu }_{\text{al}})$, with the little Bloch space of the upper half plane consisting of functions vanishing at $i$. We then investigate both the semigroup and spectral properties of the adjoint groups of composition operators which are naturally obtained from the duality pairing and are therefore defined on the identified predual.