## Annals of Functional Analysis

### $dist$-formulas and Toeplitz operators

#### Abstract

The distance from the nonconstant function $\varphi$ in $L^{\infty}% (\mathbb{T})$ to the set $\mathcal{F}_{\text{const}}$ of all constant functions is estimated in terms of Hankel operators on the Hardy space $H^{2}(\mathbb{D})$ over the unit disk $\mathbb{D}=\left\{ z\in \mathbb{C}:\left\vert z\right\vert \in [0, 1)\right\}$. We give a sufficient condition ensuring the equality $dist(\varphi,\mathcal{F}_{\text{const}})=\left\Vert \varphi\right\Vert_{L^{\infty}}$. Some other $dist$-formulas are also discussed.

#### Article information

Source
Ann. Funct. Anal., Volume 6, Number 1 (2015), 221-226.

Dates
First available in Project Euclid: 19 December 2014

https://projecteuclid.org/euclid.afa/1419001461

Digital Object Identifier
doi:10.15352/afa/06-1-16

Mathematical Reviews number (MathSciNet)
MR3297798

Zentralblatt MATH identifier
1357.47036

#### Citation

Gürdal, Mehmet; Garayev, Mübariz T.; Saltan, Suna; Yamanci, Ulaş. $dist$-formulas and Toeplitz operators. Ann. Funct. Anal. 6 (2015), no. 1, 221--226. doi:10.15352/afa/06-1-16. https://projecteuclid.org/euclid.afa/1419001461

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