I am trying to understand the second dual space and the notation in my book. The book Kreyszig defines the dual space as follows:
We define a functional $g_x$ on $X'$ by choosing a fixed $x \in X$ and setting $$g_x(f)=f(x) $$ $$(f \in X' variable)$$
What I don't understand is how $g_x (f)$ works. Is it the composition of functionals? If so, how does the composition equal $f(x)$ because wouldn't $f(x)$ give a scalar value? Thank you for any help...