Abstract
We say that x,y ∈ E are orthogonal in the Pythagorean sense, and write \( x{ \bot ^P}y \) , if ǁx + yǁ2 = ǁxǁ2 + ǁyǁ2. Some immediate properties of Pythagorean orthogonality are:
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(i)
$$ x{ \bot ^P}y \Rightarrow y{ \bot ^P}x $$
.
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© 1986 Springer Basel AG
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Amir, D. (1986). Pythagorean Type Orthogonalities. 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_8
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DOI: https://doi.org/10.1007/978-3-0348-5487-0_8
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-5489-4
Online ISBN: 978-3-0348-5487-0
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