On approximation numbers of composition operators

Details On approximation numbers of composition operators On approximation numbers of composition operators

2011-04-22

arxiv.org/abs/1104.4451v1

Mathematics

Functional Analysis

Scientific paper

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.

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