• $(x'_n)\subset X'$
• $X$ a Banach space
• $\exists x'\in X':\forall x\in X:\lim_{n\rightarrow \infty} x(x'_n)\equiv x'_n(x)=x'(x)$ .
• If $X$ is reflexive, then weak* convergence is the same as weak convergence

Note: This is a ``seed'' entry written using a short-hand format described in this FAQ.