Definition:Isometric Isomorphism/Normed Vector Space

Definition
Let $\struct {X, \norm \cdot_X}$ and $\struct {Y, \norm \cdot_Y}$ be normed vector spaces.

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

We say that $T$ is an isometric isomorphism $T$ is bijective.

If an isometric isomorphism $T : X \to Y$ exists, we say that $\struct {X, \norm \cdot_X}$ and $\struct {Y, \norm \cdot_Y}$ are isometrically isomorphic.

Also see

 * Isometric Isomorphism on Normed Vector Space is Isomorphism