A general Wolff theorem for arbitrary Banach spaces

The Kobayashi distance is used to generalise the classical theorem of Wolff to compact holomorphic fixed point free mappings on the open unit ball of an arbitrary complex Banach space E and more generally on bounded convex domains in E, thereby extending results of Abate for Cn. This is compared to earlier results on bounded symmetric domains. The boundary behaviour of the Kobayashi distance κ on bounded symmetric domains is also discussed, with estimates given for κ(z, w) as one or both of z, w tend to the boundary.