Geodesic
Isometric Mappings of Non-Commutative LP Spaces
Canadian journal of mathematics, Tome 28 (1976) no. 6, pp. 1180-1186

Voir la notice de l'article provenant de la source Cambridge University Press

If the Lp spaces of two measure spaces are “the same”, to what extent can we identify the underlying measure spaces? This question has been partially answered by Schneider [7] (extending results of Forelli [2]). He proves that a linear isometry between the Lv spaces of two finite measure spaces is in fact an (isometric) homomorphism between the corresponding L∞ spaces, if it preserves the identity. 
Katavolos, A. Isometric Mappings of Non-Commutative LP Spaces. Canadian journal of mathematics, Tome 28 (1976) no. 6, pp. 1180-1186. doi: 10.4153/CJM-1976-117-3
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