# Weak lower semicontinuity property of a bounded, coercive and linear operator

by StopUsingFacebook   Last Updated October 17, 2018 14:20 PM - source

Let $$A\colon V \to V^*$$ be a bounded linear coercive operator on a Hilbert space $$V$$.

Does it follow that for if $$u_n \rightharpoonup u$$ in $$V$$ (weak convergence) then $$\langle Au, u \rangle \leq \liminf \langle Au_n, u_n \rangle?$$

This is somehow related to weak lower semicontinuity of norms..?

Tags :