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On two classes of Banach spaces with uniform normal structure. (English) Zbl 0757.46023

The authors give two classes of Banach spaces \(X\) that have uniform normal structure. The first class is closed under duality, and contains the uniformly convex spaces as well as the uniformly smooth spaces. The second class is defined by \(J(X)<3/2\), where \[ J(X)=\sup\{\| x+y\|\wedge\| x-y\|:\;\| x\|=\| y\|=1\}. \] Both classes of spaces are uniformly nonsquare, their properties are being studied.
Reviewer: Liu Zheng (Anshan)

MSC:

46B20 Geometry and structure of normed linear spaces
46B25 Classical Banach spaces in the general theory
52A05 Convex sets without dimension restrictions (aspects of convex geometry)
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