On approximation numbers of composition operators
Functional Analysis
2011-04-25 v1
Abstract
We show that the approximation numbers of a compact composition operator on the weighted Bergman spaces 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.
Cite
@article{arxiv.1104.4451,
title = {On approximation numbers of composition operators},
author = {Daniel Li and Hervé Queffélec and Luis Rodriguez-Piazza},
journal= {arXiv preprint arXiv:1104.4451},
year = {2011}
}