Analytic approximations of uniformly continuous functions in real Banach spaces

It is shown that if a separable real Banach space X admits a separating analytic function with an additional condition (property (K), concerning uniform behaviour of radii of convergence) then every uniformly continuous mapping on X into any real Banach space Y can be approximated by analytic operators. In particular, the result applies to c(0). (C) 2001 Academic Press.