When are isometries affine 08 the examples of strictly convex spaces

When will an isometry between two norm linear spaces become an affine map (namely a translation of a linear map)? The famous Mazur-Ulam theorem tells us that it will be the case when the map is bijective. Another answer is when the target normed space is strictly convex. This video series contain the proof of these two beautiful results.

Reference: Jussi Väisälä (2003). "A Proof of the Mazur-Ulam Theorem". The American Mathematical Monthly. 110 (7): 633–635.