A lower bound on the radius of analyticity of a power series in a real Banach space
Volume 191 / 2009
Studia Mathematica 191 (2009), 171-179
MSC: 32A05, 46B99.
DOI: 10.4064/sm191-2-5
Abstract
Let $F$ be a power series centered at the origin in a real Banach space with radius of uniform convergence $\varrho$. We show that $F$ is analytic in the open ball $B$ of radius $\varrho/\sqrt{e}$, and furthermore, the Taylor series of $F$ about any point $a \in B$ converges uniformly within every closed ball centered at $a$ contained in $B$.
