Let $(E,\left \| . \right \|)$ be a Banach space and $F: E\rightarrow E$ an operator.
$F$ is said to be demi-continuous in $x$, if for any sequence $(x_n)_{n\in\mathbb{N}}$ in $E$ that converge strongly to $x$, the sequence $(T(x_n)_{n\in\mathbb{N}}$ converges weakly to $T(x)$.
It's obvious that a continuous function is demi-continuous. I look for an example of a demi-continuous function which is not continuous.
