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Compact Operators on Bergman Spaces |
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| Authors: | |
| Institution: | (1) Department of Computer Science and Mathematics, State University, 70, Arkansas, Arkansas 72467, USA;(2) Department of Mathematics, Vanderbilt University, Nashville, Tennessee 37240, USA |
| Abstract: | We prove that a bounded operator S on L a p 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. |
| Keywords: | Primary: 47B35 Secondary: 46E15 |
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