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On some Orthogonality Relations in Real Normed Spaces and Characterizations of Inner Products

C. AlsinaM.S. Tomás — 2007

Bollettino dell'Unione Matematica Italiana

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.

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