(adsbygoogle = window.adsbygoogle || []).push({}); [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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Show map is injective

**Physics Forums | Science Articles, Homework Help, Discussion**