A short exercise
Posted: Thu Jul 14, 2016 10:46 am
Let \( \displaystyle X,Y \) be Banach spaces and let \( \displaystyle T : X \longrightarrow Y \) be a surjective bounded linear operator. Show that
\[ \displaystyle \exists M>0 \; \forall y \in Y \; \exists x \in X \, : Tx = y \; \& \; ||x|| \leq M||y|| \]
\[ \displaystyle \exists M>0 \; \forall y \in Y \; \exists x \in X \, : Tx = y \; \& \; ||x|| \leq M||y|| \]