Wikipedia has a neat spaces and their duals. For example, it lists that the dual of $c_0$ is $l_1$.
But how can I use that knowledge? I'm trying to prove something for all functions of the dual of $c_0$, and figured that I could use my familiarity of $l_1$ to get some properties of those functions. But I don't know how.
For example, which element of $l_1$ corresponds to which functional of $c_0$? I suppose their "scalar product" (multiply $x\in c_0$ with $y\in l_1$ element-wise and sum the products) would be such a functional. If that's true, I could probably prove it. But I only came up with it because that was my intuition. Is there a more mechanical way?
I realize that it's hard to answer the question without knowing exactly which problem I'm trying to solve, but perhaps there are some general strategies?
Sorry if the question seems confused and "ranty"; I'm having a hard time sorting this out.