The Essential Norm of Operators on $A^p_\alpha(\mathbb{B}_n)$

Mishko Mitkovski; Daniel Suárez; Brett D. Wick

The Essential Norm of Operators on $A^p_\alpha(\mathbb{B}_n)$

Classical Analysis and ODEs 2013-01-22 v3 Complex Variables

Authors: Mishko Mitkovski , Daniel Suárez , Brett D. Wick

Abstract

In this paper we characterize the compact operators on $A^p_\alpha(\mathbb{B}_n)$ when $1<p<\infty$ and $\alpha>-1$ . The main result shows that an operator on $A^p_\alpha(\mathbb{B}_n)$ is compact if and only if it belongs to the Toeplitz algebra and its Berezin transform vanishes on the boundary of the ball.

Keywords

essential norm compact operators Toeplitz algebra Berezin transform weighted Bergman space

Cite

@article{arxiv.1204.5548,
  title  = {The Essential Norm of Operators on $A^p_\alpha(\mathbb{B}_n)$},
  author = {Mishko Mitkovski and Daniel Suárez and Brett D. Wick},
  journal= {arXiv preprint arXiv:1204.5548},
  year   = {2013}
}

Comments

v1: 32 pages; v2: 32 pages, typos corrected; v3: 32 pages, typos corrected, presentation improved based on referee comments

The Essential Norm of Operators on $A^p_\alpha(\mathbb{B}_n)$

Abstract

Keywords

Cite

Comments

Related papers