diff --git a/src/op/banach/fc.tex b/src/op/banach/fc.tex index af59ef3..9025453 100644 --- a/src/op/banach/fc.tex +++ b/src/op/banach/fc.tex @@ -130,7 +130,7 @@ \item $\exp(x) = \sum_{n = 0}^\infty \frac{x^n}{n!}$. \item $\exp(x) \in G_0(A)$ with $\exp(x)^{-1} = \exp(-x)$. \item For any $y \in A$ commuting with $x$, $\exp(x + y) = \exp(x)\exp(y)$. - \item Let $\ell: \complex \setminus (\infty, 0] \to \complex$ be the principal logarithm. If $\sigma_A(x) \subset \bracs{\lambda \in \complex| \text{Im}(\lambda) \in (-\pi, \pi)}$, then $\ell(\exp(x)) = x$. + \item Let $\ell: \complex \setminus (-\infty, 0] \to \complex$ be the principal logarithm. If $\sigma_A(x) \subset \bracs{\lambda \in \complex| \text{Im}(\lambda) \in (-\pi, \pi)}$, then $\ell(\exp(x)) = x$. \end{enumerate} \end{proposition} \begin{proof}