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

Mishko Mitkovski; Brett D. Wick

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

Complex Variables 2013-08-20 v3 Classical Analysis and ODEs Functional Analysis

Authors: Mishko Mitkovski , Brett D. Wick

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.

Keywords

Bergman space compact operators essential norm Toeplitz algebra Berezin transform polydisk

Cite

@article{arxiv.1208.5819,
  title  = {The Essential Norm of Operators on $A^p(\mathbb{D}^n)$},
  author = {Mishko Mitkovski and Brett D. Wick},
  journal= {arXiv preprint arXiv:1208.5819},
  year   = {2013}
}

Comments

v1: 45 pages. v2: 45 pages, typos corrected and presentation improved. v3: 45 pages, typos corrected based on referee comments. This paper draws heavily from arXiv:1204.5548 in order to be self-contained

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

Abstract

Keywords

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