Generalized adjoints and applications to composition operators

We generalize the classical notion of adjoint of a linear operator and the Aron-Schottenloher notion of adjoint of a homogeneous polynomial. The general (nonlinear) notion is shown to enjoy several properties enjoyed by the classical (linear) ones, nevertheless new interesting phenomena arise in the nonlinear theory. The proofs are not always simple adaptations of the linear cases, actually nonlinear arguments are often required. Applications of the generalized adjoints to Lindström-Schlüchtermann type theorems for composition operators are provided