The relations between the von Neumann-Jordan type constant and some geometric properties of Banach spaces. (English) Zbl 1515.46008
Summary: \(C_{\mathrm{NJ}}^{(p)}(X)\) and \(\widetilde{C}_{\mathrm{NJ}}^{(p)}(X)\) are generalizations of the two famous von Neumann-Jordan type constants \(C_{\mathrm{NJ}}(X)\) and \(C_{\mathrm{NJ}}^\prime(X)\), respectively. In this paper, we will analyze some properties of them and present the characterizations of uniformly non-square spaces and Hilbert spaces in terms of \(\widetilde{C}_{\mathrm{NJ}}^{(p)}(X)\). Moreover, a sufficient condition of uniform normal structure related to \(\widetilde{C}_{\mathrm{NJ}}^{(p)}(X)\) is also established.
MSC:
| 46B20 | Geometry and structure of normed linear spaces |
| 46C05 | Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product) |
Keywords:
geometric constant; von Neumann-Jordan constant; uniformly non-square space; uniform normal structureReferences:
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