Title: Approximate local isometries of derivative Hardy spaces
Abstract:For any 1 ≤ p ≤ ∞, let Sp() be the space of holomorphic functions f on such that f′ belongs to the Hardy space Hp(), with the norm ∥f∥∑ = ||f||∞ +||f′||p. We prove that every approximate local isometr...For any 1 ≤ p ≤ ∞, let Sp() be the space of holomorphic functions f on such that f′ belongs to the Hardy space Hp(), with the norm ∥f∥∑ = ||f||∞ +||f′||p. We prove that every approximate local isometry of Sp() is a surjective isometry and that every approximate 2-local isometry of Sp () is a surjective linear isometry. As a consequence, we deduce that the sets of isometric reflections and generalized bi-circular projections on Sp() are also topologically reflexive and 2-topologically reflexive.Read More
Publication Year: 2021
Publication Date: 2021-10-27
Language: en
Type: article
Indexed In: ['crossref']
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