Abstract
If orthogonality in E is symmetric then, by (18.7) and Lemma 10.4, E is smooth iff it is strictly convex. The conditions in this section characterize this case. Such are clearly:
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(19.1)
Orthogonality is symmetric and additive.
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(19.2)
Orthogonality is symmetric and unique
$$ \left( {i.e.\;x \bot y,\;x\quad \bot y\; + \;tx\; \Rightarrow t = 0} \right). $$
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© 1986 Springer Basel AG
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Amir, D. (1986). Symmetry of Orthogonality with Smoothness. In: Characterizations of Inner Product Spaces. Operator Theory: Advances and Applications, vol 20. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5487-0_20
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DOI: https://doi.org/10.1007/978-3-0348-5487-0_20
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5489-4
Online ISBN: 978-3-0348-5487-0
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