Lagrange approximation in Banach spaces

Starting from Lagrange interpolation of the exponential function e (z) in the complex plane, and using an integral representation formula for holomorphic functions on Banach spaces, we obtain Lagrange interpolating polynomials for representable functions defined on a Banach space E. Given such a representable entire funtion f: E -> a",, in order to study the approximation problem and the uniform convergence of these polynomials to f on bounded sets of E, we present a sufficient growth condition on the interpolating sequence.