Geometric mean and triangles inscribed in a semicircle in Banach spaces |
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Authors: | Javier Alonso Enrique Llorens-Fuster |
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Institution: | aDepartamento de Matemáticas, Facultad de Ciencias, Universidad de Extremadura, 06071 Badajoz, Spain;bDepartamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Valencia, Dr. Moliner, 50, 46100 Burjassot, Valencia, Spain |
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Abstract: | We consider the triangles with vertices x, −x and y where x,y are points on the unit sphere of a normed space. Using the geometric means of the variable lengths of the sides of these triangles, we define two geometric constants for Banach spaces. These constants are closely related to the modulus of convexity of the space under consideration, and they seem to represent a useful tool to estimate the exact values of the James and Jordan–von Neumann constants of some Banach spaces. |
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Keywords: | Geometry of normed spaces Convexity Modulus of convexity Uniformly non-square Banach space Normal structure |
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