On the isometries of reflexive Orlicz spaces
Annales de l'Institut Fourier, Volume 13 (1963) no. 1, p. 99-109

On obtient des expressions explicites pour les pseudo-produits scalaires (semi-inner-products) compatibles avec une norme d’Orlicz. On montre qu’un opérateur “hermitien” borné H, sur un espace réflexif d’Orlicz X, est de la forme : Hf=hf, h réelle L , et a un espace de mesure “non-atomique”. On déduit qu’une isométrie U sur X, est de la forme (Uf)(·)=u(·)f(T·), uX, T un isomorphisme mesurable d’ensembles.

@article{AIF_1963__13_1_99_0,
     author = {Lumer, Gunter},
     title = {On the isometries of reflexive Orlicz spaces},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {13},
     number = {1},
     year = {1963},
     pages = {99-109},
     doi = {10.5802/aif.132},
     zbl = {0189.43201},
     mrnumber = {28 \#1485},
     language = {en},
     url = {http://www.numdam.org/item/AIF_1963__13_1_99_0}
}
Lumer, Gunter. On the isometries of reflexive Orlicz spaces. Annales de l'Institut Fourier, Volume 13 (1963) no. 1, pp. 99-109. doi : 10.5802/aif.132. http://www.numdam.org/item/AIF_1963__13_1_99_0/

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