Abstract
A Banach space X has the Mazur–Ulam property if any isometry from the unit sphere of X onto the unit sphere of any other Banach space Y extends to a linear isometry of the Banach spaces X,Y. A Banach space X is called smooth if the unit ball has a unique supporting functional at each point of the unit sphere. We prove that each non-smooth 2-dimensional Banach space has the Mazur–Ulam property.
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