Definition:Into Linear Isomorphism

Definition
Let $\GF \in \set {\R, \C}$.

Let $X$ and $Y$ be normed vector spaces over $\GF$.

Let $T : X \to Y$ be a bounded linear transformation.

We say that $T$ is an into linear isomorphism $T$ is a linear isomorphism considered as a map $X \to T \sqbrk X$.