I remember I read those problems some place, but I cannot find it. Does anyone have any idea where I can find it?

If $X$ is a Banach space, then $(L^1(a,b;X))^*\cong L^\infty(a,b;X^*)$?

$X, Y$ are both Banach spaces, if $X$ is compactly embedded into $Y$, then do we have $L^p(a,b;X)$ is embedded in $L^p(a,b;Y)$ compactly?

If $X_1$, $X_2$ are both reflexive Banach spaces, will $(X_1, X_2)_\theta$ be reflexive?