Show that the following operators belong to the dual of $C([a, b])$, $a,b\in \mathbb{R}$ [...]
It's the beginning of a question I just read. I was wondering what exactly the dual of $C([a,b])$ is and how to check if an operator is in the dual of a space.
I know that the dual space of $X$ is the space of all linear maps from $X\rightarrow \mathbb{K}$. So in this case all linear maps from $C([a,b]) \rightarrow \mathbb{R}$?