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On Birkhoff orthogonality and isosceles orthogonality in normed linear spaces. (English) Zbl 1241.46006

Summary: We survey mainly recent results on the two most important orthogonality types in normed linear spaces, namely on Birkhoff orthogonality and on isosceles (or James) orthogonality. We lay special emphasis on their fundamental properties, on their differences and connections, and on geometric results and problems inspired by the respective theoretical framework. At the beginning we also present other interesting types of orthogonality. This survey can also be taken as an update of existing related representations.

MSC:

46B20 Geometry and structure of normed linear spaces
46C15 Characterizations of Hilbert spaces
52A21 Convexity and finite-dimensional Banach spaces (including special norms, zonoids, etc.) (aspects of convex geometry)
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