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COMPACT TOEPLITZ OPERATORS

  • Received : 2013.03.06
  • Accepted : 2013.03.20
  • Published : 2013.09.25

Abstract

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

Keywords

weighted Bergman spaces;Toeplitz operators;self-adjoint;Hilbert-Schmidt;compact operators

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