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Rectangular modulus, Birkhoff orthogonality and characterizations of inner product spaces

Ioan Şerb (1999)

Commentationes Mathematicae Universitatis Carolinae

Some characterizations of inner product spaces in terms of Birkhoff orthogonality are given. In this connection we define the rectangular modulus μ X of the normed space X . The values of the rectangular modulus at some noteworthy points are well-known constants of X . Characterizations (involving μ X ) of inner product spaces of dimension 2 , respectively 3 , are given and the behaviour of μ X is studied.

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