Overview
Given two normed vector spaces {% X %} and {% Y %}, an isometry is an operator
{% T: X \rightarrow Y %}
such that
{% || T(x) || = || x || %}
Theorems
- For normed linear spaces {% X %} and {% Y %} and bounded linear operator {% T : X \rightarrow Y %}, {% T %} is an isometry implies that {% T %} is bounded and {% || T || = 1 %}