On the stability index for weighted composition operators

Let epsilon > 0. A continuous linear operator T : C(X) -> C(Y) is said to E-preserve disjointness if parallel to(Tf)(Tg)parallel to infinity <= epsilon, whenever f,g is an element of C(X) satisfy parallel to f parallel to infinity = parallel to g parallel to infinity = I and fg 0. In this paper we continue our study of the minimal interval where the possible maximal distance from a norm one operator which E-preserves disjointness to the set of weighted composition maps may lie. We provide sharp bounds for both the finite and the infinite case, which turn out to be completely different. (C) 2010 Elsevier Inc. All rights reserved.