This paper generalizes the special case of the Carlsson orthogonality in terms of the 2-HH norm in real normed linear space. Dragomir and Kikianty (2010) proved in their paper that the Pythagorean orthogonality is unique in any normed linear space, and isosceles orthogonality is unique if and only if the space is strictly convex. This paper deals with the complete proof of the uniqueness of the new orthogonality through the medium of the 2-HH norm. We also proved that the Birkhoff and Robert orthogonality via the 2-HH norm are equivalent, whenever the underlying space is a real inner-product space.

中文翻译：

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赋范空间中基于2-HH范数的新正交性的唯一性

本文以实数范数线性空间中的2-HH范数概括了Carlsson正交性的特殊情况。Dragomir and Kikianty（2010）在他们的论文中证明，毕达哥拉斯正交性在任何赋范线性空间中都是唯一的，等腰正交性在且仅当空间严格凸时才是唯一的。本文以2-HH范数为媒介，全面证明了新正交性的唯一性。我们还证明了，只要下层空间是真实的内积空间，通过2-HH范数的Birkhoff和Robert正交性是等效的。