Isometries of Musielak-Orlicz spaces II

A characterization of isometries of complex Musielak-Orlicz spaces ${\displaystyle L_{\Phi }}$ is given. If ${\displaystyle L_{\Phi }}$ is not a Hilbert space and ${\displaystyle U:L_{\Phi }\to L_{\Phi }}$ is a surjective isometry, then there exist a regular set isomorphism τ from (T,Σ,μ) onto itself and a measurable function w such that U(f) = w ·(f ∘ τ) for all ${\displaystyle f\in L_{\Phi }}$. Isometries of real Nakano spaces, a particular case of Musielak-Orlicz spaces, are also studied.