Relatively weakly open sets in closed balls of Banach spaces, and real JB*-triples of finite rank
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- Guerrero, J., Pérez, G., Peralta, A. et al. Math. Ann. (2004) 330: 45. doi:10.1007/s00208-004-0537-y
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We prove that, given a real JB*-triple X, there exists a nonempty relatively weakly open subset of the closed unit ball of X with diameter less than 2 (if and) only if the Banach space of X is isomorphic to a Hilbert space. Moreover we give the structure of real JB*-triples whose Banach spaces are isomorphic to Hilbert spaces. Such real JB*-triples are also characterized in two different purely algebraic ways.