# Try to find a seminorm $p$ on a locally convex space st $|f|\leq p$.

Let $X$ be a locally convex space. Let $M$ be a linear subspace of a locally convex space $X$. Let $f\in M^*$. Then can we find a seminorm $p$ on $X$ such that $|f(x)|\leq p(x)$ for all $x\in M$?

• Isn't $|f|$ a seminorm? – Lord Shark the Unknown Sep 6 '18 at 18:18
• @LordSharktheUnknown Yes but it is not on $X$. – Answer Lee Sep 6 '18 at 18:18
• Then extend $f$ it to $X$. – Lord Shark the Unknown Sep 6 '18 at 18:21