论文标题
严格凸重态和直径2属性
Strictly convex renormings and the diameter 2 property
论文作者
论文摘要
据说Banach空间（或其规范）具有直径$ 2 $的属性（D $ 2 $ P），如果其封闭单位球的每个非空地相对较弱的开放子集的直径为$ 2 $，则具有直径$ 2 $ p。我们在$ l_1 [0,1] $上构建同等标准，该标准在本地均匀圆形且具有D $ 2 $ p的情况下是弱的。我们还证明，对于Banach的空间，承认一个规范性的有限co维投影，不可能在各个方向上均匀地旋转，同时又有D $ 2 $ p。
A Banach space (or its norm) is said to have the diameter $2$ property (D$2$P in short) if every nonempty relatively weakly open subset of its closed unit ball has diameter $2$. We construct an equivalent norm on $L_1[0,1]$ which is weakly midpoint locally uniformly rotund and has the D$2$P. We also prove that for Banach spaces admitting a norm-one finite-co-dimensional projection it is impossible to be uniformly rotund in every direction and at the same time have the D$2$P.
