Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Geometric and probabilistic estimates for entropy and approximation numbers of operators
Journal of Approximation Theory
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We show that the approximation numbers of a compact composition operator on the Hardy space H^2 or on the weighted Bergman spaces B"@a of the unit disk can tend to 0 arbitrarily slowly, but that they never tend quickly to 0: they cannot decay more rapidly than exponentially, and this speed of convergence is only obtained for symbols which do not approach the unit circle. We also give an upper bound and explicit an example.