Isometries of Musielak-Orlicz spaces II
Tom 104 / 1993
Studia Mathematica 104 (1993), 75-89
DOI: 10.4064/sm-104-1-75-89
Streszczenie
A characterization of isometries of complex Musielak-Orlicz spaces $L_Φ$ is given. If $L_Φ$ is not a Hilbert space and $U : L_Φ → L_Φ$ 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 $f ∈ L_Φ$. Isometries of real Nakano spaces, a particular case of Musielak-Orlicz spaces, are also studied.
