Reflexivity of Lp spaces
= Reflexivity of Lp spaces
{c}
For $1<p<\infty$, the identifications $(L^p)^*=L^q$ and $(L^q)^*=L^p$ make $L^p$ reflexive. On a non-atomic space such as $\mathbb R^n$, neither $L^1$ nor $L^\infty$ is reflexive.
= Reflexivity of Lp spaces
{c}
For $1<p<\infty$, the identifications $(L^p)^*=L^q$ and $(L^q)^*=L^p$ make $L^p$ reflexive. On a non-atomic space such as $\mathbb R^n$, neither $L^1$ nor $L^\infty$ is reflexive.