Definition:Isometric Isomorphism/Normed Vector Space

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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 if and only if $T$ 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

  • Results about isometric isomorphisms on normed vector spaces can be found here.


Sources