Isometries of Musielak-Orlicz Spaces

Abstract

Introduction. In 1932, S. Banach in his monograph [2], gave a characterization of isometries in Lp , for 1 < ρ < ⊂, ρ Φ 2. A different proof and a partial generalization to Orlicz spaces of this result, was given by J.Lamperti in [9]. In 1963, G.Lumer ([10]) made an important step in studying isometries. He introduced a new method for complex spaces, based on Hermitian operators. In fact, he applied Hermitian operators to find a characterization of isometries in reflexive Orlicz spaces. His method has become a fruitful tool for further studies and generalizations. Thus, e.g. in [14], [5], [1], [4], the authors characterized isometries in vector valued function spaces or complex sequence spaces, via Hermitian operators. In [15], [16], M.G.Zaidenberg found a description of isometries in Orlicz and symmetric spaces, without assumptions of reflexivity or separability, generalizing essentially Lumer’s result.