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On angular measures in Minkowski planes. (English) Zbl 1246.46011

Following ideas of Brass and Düvelmeyer, the author introduces a translation invariant angular measure for normed planes that has the property that if two James-orthogonal vectors form an angle of measure \({\pi\over 2}\), then the plane is Euclidean. This implication does not hold for Birkhoff orthogonality; it yields a more general class of norms whose unit circles suitably contain arcs which are pieces of Radon curves.

MSC:

46B20 Geometry and structure of normed linear spaces
52A21 Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry)
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References:

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