Compact and weakly compact composition operators on BMOA
Functional Analysis
2010-01-22 v2 Complex Variables
Abstract
We show that a composition operator induced by an analytic self-map of the unit disc in the complex plane is weakly compact on the space BMOA precisely when the operator is compact on BMOA. As a crucial step we simplify the compactness criterion due to Smith for composition operators on BMOA and show that his condition on the Nevanlinna counting function alone characterizes compactness. In addition, other equivalent compactness criteria are established for composition operators on both BMOA and its subspace VMOA.
Keywords
Cite
@article{arxiv.0912.3487,
title = {Compact and weakly compact composition operators on BMOA},
author = {Jussi Laitila and Pekka J. Nieminen and Eero Saksman and Hans-Olav Tylli},
journal= {arXiv preprint arXiv:0912.3487},
year = {2010}
}