# Prob. 11, Sec. 2.10 in Erwin Kreyszig's book

If $X$ is a normed space and dim $x=\infty$, show that the dual space $X'$ (set of all bounded linear functionals on $X$) is not identical with algebraic dual space $X^*$ (set of all linear functionals on $X$)

that there is at least one element $T\in X^*$ that is not in $X'$