Given Banach spaces$V$ and $W$, a short linear map form $V$ to $W$ is a (total) function$f\colon V \to W$ that is both short and linear, equivalently a bounded linear operator whose norm is at most $1$. These are also called contractive (or weakly contractive) linear maps; they may also be called short (or contractive or weakly contractive) operators (with linearity usually assumed but sometimes mentioned), or even simply (weak) contractions.