[SOLVED] Show map is injective 1. The problem statement, all variables and given/known data Going crazy over this. Let 1<p<2 and q>=2 be its conjugate exponent. I want to show that the map T: L^p(E) --> (L^q(E))*: x-->T(x) where [tex]<T(x),y> = \int_Ex(t)y(t)dt[/tex] is injective. This amount to showing that if [tex]\int_Ex(t)y(t)dt=0[/tex] for all q-integrable functions y(t), then x(t)=0 (alsmost everywhere) Should be easy but I've been at this for an hour and I don't see it!