Geodesic
On some Orthogonality Relations in Real Normed Spaces and Characterizations of Inner Products
Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 513-520.

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Using some functionals which fulfil much more general requirements than the usual axioms of inner products and by considering some weak versions of orthogonal relations in real normed spaces we find new characterizations of inner products in the cases of James and Pythagoras orthogonalities but we show that this is not the case when Birkhoff orthogonality is postulated.
Usando alcuni funzionali soddisfacenti condizioni molto più generali degli usuali assiomi dei prodotti scalari e considerando alcune deboli versioni delle relazioni di ortogonalità negli spazi reali normati, troviamo nuove caratterizzazioni dei prodotti scalari nei casi di ortogonalità di James e di Pitagora, ma non nel caso dell'ortogonalità di Birkhoff. 
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Alsina, C.; Tomás, M.S. On some Orthogonality Relations in Real Normed Spaces and Characterizations of Inner Products. Bollettino della Unione matematica italiana, Série 8, 10B (2007) no. 3, pp. 513-520. http://geodesic.mathdoc.fr/item/BUMI_2007_8_10B_3_a0/

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