Geometric mean and triangles inscribed in a semicircle in Banach spaces. (English) Zbl 1153.46007
Let \(X\) be a Banach space with the unit sphere \(S_X:=\{x\in X:\| x\| =1\}\). The authors introduce the two new constants \(t(X)=\inf_{x\in S_X}\sup_{y\in S_X}\sqrt{\| x+y\| \| x-y\| }\) and \(T(X)=\sup_{x,y\in S_X}\sqrt{\| x+y\| \| x-y\| }\). They give some relationships between these constants and other known ones, e.g., the James and von Neumann–Jordan constants. The exact values of these constants are computed for some interesting Banach spaces.
Reviewer: Satit Saejung (Khon Kaen)
MSC:
| 46B20 | Geometry and structure of normed linear spaces |
Keywords:
geometry of normed spaces; modulus of convexity; uniformly non-square Banach space; normal structureReferences:
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