I have a question about the differential of a function between two normed spaces. It is a simple question about the definition.
In my textbook from my university, the definition is as follows:
Let $E$ an $F$ be normed spaces, $U \subset E$ open and $f:U \rightarrow F$. f is called differentiable in $a \in U$, if there exists a continuous, linear map $L:E \rightarrow F$, for which, with $||h||$ sufficient smal,
$\qquad$ $\qquad$ $\qquad$$\qquad$$\qquad$$f(a+h) = f(a) + L*h +o(h), \qquad h \rightarrow 0$
Could it be this is wrong?
If I search for it online, I often find $L(h)$ instead of $L*h$