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arXiv · 1901.02737

Surjective isometries on a Banach space of analytic functions with bounded derivatives

Takeshi Miura·Norio Niwa
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Abstract

Let $H(\mathbb{D})$ be the linear space of all analytic functions on the open unit disc $\mathbb{D}$ and $H^p(\mathbb{D})$ the Hardy space on $\mathbb{D}$. The characterization of complex linear isometries on $\mathcal{S}^p=\{f\in H(\mathbb{D}):f'\in H^p(\mathbb{D})\}$ was given for $1\leq p<\infty$ by Novinger and Oberlin in 1985. Here, we characterize surjective, not necessarily linear, isometries on $\mathcal{S}^\infty$.

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Takeshi Miura, Norio Niwa. 2019-01-09. Surjective isometries on a Banach space of analytic functions with bounded derivatives. https://arxiv.org/abs/1901.02737

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