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Compact Operators on Bergman Spaces

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Abstract.

We prove that a bounded operator S on L p a for p > 1 is compact if and only if the Berezin transform of S vanishes on the boundary of the unit disk if S satisfies some integrable conditions. Some estimates about the norm and essential norm of Toeplitz operators with symbols in BT are obtained.

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Authors and Affiliations

  1. Department of Computer Science and Mathematics, State University, 70, Arkansas, Arkansas, 72467, USA

    Jie Miao

  2. Department of Mathematics, Vanderbilt University, Nashville, Tennessee, 37240, USA

    Dechao Zheng

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  1. Jie Miao
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  2. Dechao Zheng
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Correspondence to Jie Miao.

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Miao, J., Zheng, D. Compact Operators on Bergman Spaces. Integr. equ. oper. theory 48, 61–79 (2004). https://doi.org/10.1007/s00020-002-1176-x

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  • DOI: https://doi.org/10.1007/s00020-002-1176-x

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