Abstract
Let C (1)([0, 1]) be the Banach space of continuously differentiable functions on the closed unit interval [0, 1] equipped with the norm ||f||σ= | f (0)| +|| f ′||∞, where ||g||∞= sup{|g(t)| : t ∈ [0, 1]} for g. If T : C (1) ([0, 1]) → C (1) ([0, 1]) is a 2-local real-linear isometry, then T is a surjective real-linear isometry.
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