The Essential Norm of Operators on $A^p(\mathbb{D}^n)$

Mishko Mitkovski; Brett D. Wick

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arXiv · 1208.5819

The Essential Norm of Operators on $A^p(\mathbb{D}^n)$

Mishko Mitkovski·Brett D. Wick

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Abstract

In this paper we characterize the compact operators on the Bergman space $A^p(\mathbb{D}^n)$. The main result shows that an operator on $A^p(\mathbb{D}^n)$ is compact if and only if it belongs to the Toeplitz algebra $\mathcal{T}_{p}$ and its Berezin transform vanishes on the boundary.

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BibTeX RIS

Mishko Mitkovski, Brett D. Wick. 2012-08-29. The Essential Norm of Operators on $A^p(\mathbb{D}^n)$. https://arxiv.org/abs/1208.5819

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