On the functional equation defined by Lie's product formula
Volume 175 / 2006
Studia Mathematica 175 (2006), 271-277
MSC: 39B52, 46H99.
DOI: 10.4064/sm175-3-5
Abstract
Let $E$ be a real normed space and ${\cal A}$ a complex Banach algebra with unit. We characterize the continuous solutions $f:E \to {\cal A}$ of the functional equation $f(x+y)=\lim_{n \to \infty} (f(x/n)f(y/n))^n$.
