Banach Journal of Mathematical Analysis

Certain distance estimates for operators on the Bergman space

Namita Das and Madhusmita Sahoo

Full-text: Open access

Abstract

Let $\mathbb{D}$ be the open unit disk with its boundary $\partial\mathbb{D}$ in the complex plane $\mathbb{C}$ and $dA(z)=\frac{1}{\pi}dx\, dy,$ the normalized area measure on $\mathbb{D}.$ Let $L_{a}^{2}(\mathbb{D}, dA)$ be the Bergman space consisting of analytic functions on $\mathbb{D}$ that are also in $L^2(\mathbb{D}, dA).$ In this paper we obtain certain distance estimates for bounded linear operators defined on the Bergman space.

Article information

Source
Banach J. Math. Anal., Volume 8, Number 2 (2014), 193-203.

Dates
First available in Project Euclid: 4 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1396640063

Digital Object Identifier
doi:10.15352/bjma/1396640063

Mathematical Reviews number (MathSciNet)
MR3189550

Zentralblatt MATH identifier
1303.47029

Subjects
Primary: 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.)
Secondary: 47B35: Toeplitz operators, Hankel operators, Wiener-Hopf operators [See also 45P05, 47G10 for other integral operators; see also 32A25, 32M15]

Keywords
Bergman space positive operators Toeplitz operators bounded harmonic functions distance estimates

Citation

Das, Namita; Sahoo, Madhusmita. Certain distance estimates for operators on the Bergman space. Banach J. Math. Anal. 8 (2014), no. 2, 193--203. doi:10.15352/bjma/1396640063. https://projecteuclid.org/euclid.bjma/1396640063


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