How to prove the space of bounded linear functionals in a linear norm space is complete?
I just have no idea how to use assumptions about $f_n$ to prove $f$ is bounded? I do it like this,
Main idea is since $f_n$ is Cauchy sequence exist N , when $n,m>N$,$||f_n-f_m||<\epsilon$
$f_n$ is bounded,$||fn||<C_n$,then $||f||<\epsilon+C_n$ ,also bounded.
Is this right?