Diameter 2 Properties and Convexity

Trond Arnold Abrahamsen,Petr Hajek,Olav Nygaard,Jarno Talponen,Stanimir Troyanski

Studia Mathematica（2016）

引用 6|浏览17

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摘要

We present an equivalent midpoint locally uniformly rotund (MLUR) renorming of C[0, 1] with the diameter 2 property (D2P), i.e. every non-empty relatively weakly open subset of the unit ball has diameter 2. An example of an MLUR space with the D2P and with convex combinations of slices of arbitrarily small diameter is also given.

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关键词

diameter 2 property,midpoint locally uniformly rotund,Daugavet property

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