Research Article

Approximate local isometries of derivative Hardy spaces

Published in: Quaestiones Mathematicae
Volume 46 , issue 1 , 2023 , pages: 23–34

DOI: 10.2989/16073606.2021.1985007

Author(s): A. Jiménez-Vargas Universidad de Almería, Spain , Takeshi Miura Niigata University, Japan

Keywords: 47B38 , 47B33 , 46B04 , Algebraic reflexivity , topological reflexivity , isometry group , isometric reflection

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Abstract

For any 1 ≤ p ≤ ∞, let S^p () be the space of holomorphic functions f on such that f′ belongs to the Hardy space H^p (), with the norm ∥f∥_∑ = ||f||_∞ +||f′|| _p . We prove that every approximate local isometry of S^p () is a surjective isometry and that every approximate 2-local isometry of S^p () is a surjective linear isometry. As a consequence, we deduce that the sets of isometric reflections and generalized bi-circular projections on S^p () are also topologically reflexive and 2-topologically reflexive.

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