On local isometries between algebras of C(Y)-valued differentiable maps
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2022-05-18Abstract
Let K be either the real unit interval [0,1] or the complex unit circle 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 sum-norm, is topologically reflexive and 2-topologically reflexive whenever the isometry group of C(Y) is topologically reflexive.
Palabra/s clave
Algebraic reflexivity
Topological reflexivity
Local isometry
2-local isometry
Differentiable map