I read article New Sequential Compactness Results for Spaces of Scalarly Integrable Functions by Erik J. Balder, on page 8 : Author defined the function $a: T\times E\to \mathbb{R}$ by the usual duality between $E$ and $E^*=F$ $( ⟨.,.⟩)$ such that: $$ a(t,x)=\langle x, t\rangle $$ But normally the second variable $(t\in T)$ must be an element of dual of $E$, right? Why does the author make this notation?
An idea please
