Abstract
We introduce three concepts, called $I$-vector, $IP$-vector, and $P$-vector, which are related to isosceles orthogonality and Pythagorean orthogonality in normed linear spaces. Having the Banach-Mazur rotation problem in mind, we prove that an almost transitive real Banach space, whose dimension is at least three and which contains an $I$-vector (an $IP$-vector, a $P$-vector, or a unit vector whose pointwise James constant is $\sqrt2$, respectively) is a Hilbert space.
Citation
Horst Martini. Senlin Wu. "Orthogonalities, transitivity of norms and characterizations of Hilbert spaces." Rocky Mountain J. Math. 45 (1) 287 - 301, 2015. https://doi.org/10.1216/RMJ-2015-45-1-287
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