Reflexive space

Summary

A normed space is reflexive when the canonical embedding into its bidual is onto. Reflexive spaces are always Banach spaces. They are the Banach spaces whose closed unit ball is weakly compact. So bounded sequences have weakly convergent subsequences, which makes them the natural setting for existence proofs by minimization. Hilbert spaces, $L^p$ spaces for $1 < p < \infty$ and finite-dimensional spaces are reflexive.