# topological vector spaces – Weak\$^*\$ continous functionals

Let $$X$$ be a Banach space (not necessarily reflexive) and let $$X^{*}$$ denote the continuous dual of $$X$$. Let $$psi:X to X^{**}$$ denote the canonical embedding of $$X$$ into its double dual $$X^{**}$$. We know that the weak$$^*$$ topology on $$X^*$$ is induced by the family of continuous linear functionals $${psi(x): xin X}$$.

From this, can we say that every weak$$^*$$ continuous linear functional on $$X^*$$ is of the form $$psi(x)$$ for some $$xin X$$? If it is, I would like to know an explanation of the answer. If not then a counter example would help. I am a beginner on this domain and know very little. So, I do not know, if this question is trivial.