Abstract
Let K be either the real unit interval [0, 1] or the complex unit circle {mathbb {T}} and let C(Y) be the space of all complex-valued continuous functions on a compact Hausdorff space Y. We prove that the isometry group of the algebra C^1(K,C(Y)) of all C(Y)-valued continuously differentiable maps on K, equipped with the Sigma -norm, is topologically reflexive and 2-topologically reflexive whenever the isometry group of C(Y) is topologically reflexive.
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