In this paper we introduce two classes of operators on spaces of continuous functions
with values in F-spaces under the action of which many functions behave chaotically
near the boundary. Several examples, including onto linear operators, left and right
composition operators, multiplication operators, and operators with pointwise dense range or with some stability property, are given. This new theory extends one recently
developed on spaces of holomorphic functions.Plan Andaluz de Investigación (Junta de Andalucía
