Bárcenas, Diomedes The Minkowski plane and the geometry of Banach spaces. (Spanish. English summary) Zbl 1186.46013 Bol. Asoc. Mat. Venez. 15, No. 1, 111-129 (2008). 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 Keywords:structure of a Banach space; two-dimensional subspaces PDFBibTeX XMLCite \textit{D. Bárcenas}, Bol. Asoc. Mat. Venez. 15, No. 1, 111--129 (2008; Zbl 1186.46013) Full Text: EuDML