Geodesic
Rectangular modulus, Birkhoff orthogonality and characterizations of inner product spaces
Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 1, pp. 107-119.

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Some characterizations of inner product spaces in terms of Birkhoff orthogonality are given. In this connection we define the rectangular modulus $\mu_{_X}$ of the normed space $X$. The values of the rectangular modulus at some noteworthy points are well-known constants of $X$. Characterizations (involving $\mu_{_X})$ of inner product spaces of dimension $\geq 2$, respectively $\geq 3$, are given and the behaviour of $\mu_{_X}$ is studied.
Classification : 46B04, 46B20, 46C15
Keywords: characterizations of inner product spaces; orthogonality; moduli of Banach spaces 
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Şerb, Ioan. Rectangular modulus, Birkhoff orthogonality and characterizations of inner product spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) no. 1, pp. 107-119. http://geodesic.mathdoc.fr/item/CMUC_1999__40_1_a7/