Schauder's theorem
$\textbf{Schauder's theorem}$
A bounded linear operator from a Banach space into a Banach space is compact if and only if its adjoint is compact.
𝐒𝐜𝐡𝐚𝐮𝐝𝐞𝐫’𝐬 𝐭𝐡𝐞𝐨𝐫𝐞𝐦
A bounded linear operator from a Banach space into a Banach space is compact if and only if its adjoint is compact.