6533b831fe1ef96bd12984b2

RESEARCH PRODUCT

Geometric mean and triangles inscribed in a semicircle in Banach spaces

Javier AlonsoEnrique Llorens-fuster

subject

Unit sphereUniformly non-square Banach spacePure mathematicsApplied MathematicsMathematical analysisBanach spaceUniformly convex spaceBanach manifoldModulus of convexitySpace (mathematics)Normal structureConvexityGeometry of normed spacesInterpolation spaceLp spaceAnalysisNormed vector spaceMathematics

description

AbstractWe 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.

yearjournalcountryeditionlanguage
2008-04-01Journal of Mathematical Analysis and Applications
10.1016/j.jmaa.2007.09.040http://dx.doi.org/10.1016/j.jmaa.2007.09.040