Category:Isometric Isomorphisms (Normed Vector Spaces)

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This category contains results about isometric isomorphisms in the context of Normed Vector Spaces.
Definitions specific to this category can be found in Definitions/Isometric Isomorphisms (Normed Vector Spaces).

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.