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 if and only if $T$ is a linear isomorphism considered as a map $X \to T \sqbrk X$.

Sources

• 2001: Marián Fabian, Petr Habala, Petr Hájek, Vicente Montesinos Santalucía, Jan Pelant and Václav Zizler: Functional Analysis and Infinite-Dimensional Geometry ... (previous) ... (next): Proposition $1.19$