Radius of analyticity of analytic functions on Banach spaces

We examine the question of when the radius of analyticity of a real analytic function on a real Banach space is equal to its radius of uniform convergence. We will see that a positive solution to this problem on ℓ1 implies a positive solution on all Banach spaces. In the final section we show that our question has an affirmative answer for power series of positive polynomials on Banach lattices.