Approximate local isometries of derivative Hardy spaces
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2021-10-27Abstract
For any p in [1,\infty], let S^p(D) be the space of holomorphic functions f on D such that f' belongs to the Hardy space H^p(D), with the sum norm. We prove that every approximate local isometry of S^p(D) is a surjective isometry and that every approximate 2-local isometry of S^p(D) is a surjective linear isometry. As a consequence, we deduce that the sets of isometric reflections and generalized bi-circular projections on S^p(D) are also topologically reflexive and 2-topologically reflexive.
Palabra/s clave
Algebraic reflexivity
Topological reflexivity
Isometry group
Isometric reflection