Composition Operators on Banach Function Spaces

We study the boundedness and the compactness of composition operators on some Banach function spaces such as absolutely continuous Banach function spaces on a σ \sigma –finite measure space, Lorentz function spaces on a σ \sigma –finite measure space and rearrangement invariant spaces on a resonant measure space. In addition, we study some properties of the spectra of a composition operator on the general Banach function spaces.