Stability of weighted composition operators between spaces of continuous functions

摘要

Let ϵ>0. A continuous linear operator T:C(X)→C(Y) is said to be ϵ-disjointness preserving if ‖ (Tf)(Tg)‖∞≤ϵ whenever f, g∈C(X) satisfy ‖ f‖∞=‖ g‖∞=1 and fg≡ 0. In this paper we basically address the following question: How close must weighted composition operators be to a given ϵ-disjointness preserving operator?We provide sharp stability bounds.