Annals of Functional Analysis

$dist$-formulas and Toeplitz operators

Mübariz T. Garayev, Mehmet Gürdal, Suna Saltan, and Ulaş Yamanci

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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

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

First available in Project Euclid: 19 December 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B35
Secondary: 47B10: Operators belonging to operator ideals (nuclear, p-summing, in the Schatten-von Neumann classes, etc.) [See also 47L20]

Hardy space Hankel operator Toeplitz operator Maximal numerical range $dist$-formula


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.

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