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.
@article{119066,
author = {Ioan \c Serb},
title = {Rectangular modulus, Birkhoff orthogonality and characterizations of inner product spaces},
journal = {Commentationes Mathematicae Universitatis Carolinae},
volume = {40},
year = {1999},
pages = {107-119},
zbl = {1060.46506},
mrnumber = {1715205},
language = {en},
url = {http://dml.mathdoc.fr/item/119066}
}
Şerb, Ioan. Rectangular modulus, Birkhoff orthogonality and characterizations of inner product spaces. Commentationes Mathematicae Universitatis Carolinae, Tome 40 (1999) pp. 107-119. http://gdmltest.u-ga.fr/item/119066/
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