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The Minkowski plane and the geometry of Banach spaces. (Spanish. English summary) Zbl 1186.46013

Summary: We explain how some properties of Banach spaces can be obtained from the study of the two-dimensional subspaces; especially, we study some characterizations of Hilbert spaces, uniformly convex, strictly convex, and smooth spaces. We also show how to obtain information of the normal structure of a Banach space from its two-dimensional subspaces.

MSC:

46B20 Geometry and structure of normed linear spaces
46C15 Characterizations of Hilbert spaces
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