Quotient Map is a Contraction Operator

Last updated Nov 1, 2022

Let $(X, ||\cdot||)$ be a Banach Space and let $Y \subset X$ be a Closed Vector Subspace. Then the Quotient Map $J : X \to X / Y$ defined as $J(x) := [x]$ is a Bounded Linear Operator and $||J|| \leq 1$.

• Operator Norm