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

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Abstract

In this paper we characterize the compact operators on the weighted Bergman spaces \({A^p_\alpha(\mathbb{B}_n)}\) when 1 < p < ∞ and α > −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.

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Correspondence to Brett D. Wick.

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M. Mitkovski supported in part by National Science Foundation DMS grant # 1101251; D. Suárez supported in part by the ANPCyT grant PICT2009-0082, Argentina; B.D. Wick supported in part by National Science Foundation DMS grants # 1001098 and # 0955432.

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Mitkovski, M., Suárez, D. & Wick, B.D. The Essential Norm of Operators on \({A^p_\alpha(\mathbb{B}_n)}\) . Integr. Equ. Oper. Theory 75, 197–233 (2013). https://doi.org/10.1007/s00020-012-2025-1

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