Geodesic
A Generalization of Uniformly Rotund Banach Spaces
Canadian journal of mathematics, Tome 31 (1979) no. 3, pp. 628-636

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

Let X be a real Banach space. According to von Neumann's famous geometrical characterization X is a Hilbert space if and only if for all x, y ∈ X Thus Hilbert space is distinguished among all real Banach spaces by a certain uniform behavior of the set of all two dimensional subspaces. A related characterization of real L p spaces can be given in terms of uniform behavior of all two dimensional subspaces and a Boolean algebra of norm-1 projections [16]. For an arbitrary space X, one way of measuring the “uniformity” of the set of two dimensional subspaces is in terms of the real valued modulus of rotundity, i.e. for The space is said to be uniformly rotund if for each 0 we have . 
Sullivan, Francis. A Generalization of Uniformly Rotund Banach Spaces. Canadian journal of mathematics, Tome 31 (1979) no. 3, pp. 628-636. doi: 10.4153/CJM-1979-063-9
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