COMPACT TOEPLITZ OPERATORS

• Journal title : Honam Mathematical Journal
• Volume 35, Issue 3,  2013, pp.343-350
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2013.35.3.343
Title & Authors
COMPACT TOEPLITZ OPERATORS
Kang, Si Ho;

Abstract
In this paper we prove that if Toeplitz operators $\small{T^{\alpha}_u}$ with symbols in RW satisfy $\small{{\parallel}uk^{\alpha}_z{\parallel}_{s,{\alpha}{\rightarrow}0}$ as $\small{z{\rightarrow}{\partial}\mathbb{D}}$ then $\small{T^{\alpha}_u}$ is compact and also prove that if $\small{T^{\alpha}_u}$ is compact then the Berezin transform of $\small{T^{\alpha}_u}$ equals to zero on $\small{{\partial}\mathbb{D}}$.
Keywords
Language
English
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