I am studying functional analysis and I was asked to prove that $c_0$ is not reflexive. The point is I have no idea how to prove this. I don't even know how to show that a space is reflexive. What must I do on the practice?
I think it is hard to solve this kind of problem just looking for the canonical embedding and trying to discover it is surjective since several times we don't have any idea of which space is the bidual to our space.
My question is, what are useful theorems and techniques in order to show a space is/or not is, reflexive?