## Nihonkai Mathematical Journal

### Surjective isometries on a Banach space of analytic functions on the open unit disc

#### Abstract

Let $\mathcal{S}_A$ be the complex linear space of all analytic functions on the open unit disc $\mathbb D$, whose derivative can be extended to the closed unit disc $\bar{\mathbb D}$. We give the characterization of surjective, not necessarily linear, isometries on $\mathcal{S}_A$ with respect to the norm $\| f \| _{\sigma} = |f(0)| + \sup \{|f'(z)| : z \in \mathbb D \}$ for $f \in \mathcal{S}_A$.

#### Note

The authors are thankful to an anonymous referee for suggestions that improved our results.

#### Article information

Source
Nihonkai Math. J., Volume 29, Number 1 (2018), 53-67.

Dates
Revised: 14 June 2018
First available in Project Euclid: 6 February 2019

https://projecteuclid.org/euclid.nihmj/1549422084

Mathematical Reviews number (MathSciNet)
MR3908819

Zentralblatt MATH identifier
07063841

#### Citation

Miura, Takeshi; Niwa, Norio. Surjective isometries on a Banach space of analytic functions on the open unit disc. Nihonkai Math. J. 29 (2018), no. 1, 53--67. https://projecteuclid.org/euclid.nihmj/1549422084

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