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On approximation numbers of composition operators

By Daniel Li, Hervé Queffélec and Luis Rodriguez-Piazza


We show that the approximation numbers of a compact composition operator on the weighted Bergman spaces $\mathfrak{B}_\alpha$ of the unit disk can tend to 0 arbitrarily slowly, but that they never tend quickly to 0: they grow at least exponentially, and this speed of convergence is only obtained for symbols which do not approach the unit circle. We also give an upper bounds and explicit an example

Topics: Mathematics - Functional Analysis
Year: 2011
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