Spaces of Θ-faintly and α-faintly continuous functions and composition operators

Abstract

This work is dedicated to the study of composition operator C_φ where φ is a continuous function. First, we characterize topologies on C^θ(X,Y), the space of θ-faintly continuous, to establish results for the composition operator C_φ, acting between spaces of θ-faintly continuous functions. Next, topologies on C^α(X,Y), the space of α-faintly continuous, are analyzed in the same way to obtain results again for the composition operator C_φ. In both cases, weak, strong and exponential topologies are investigated, obtaining inclusion properties and where the evaluation map is key.