Daugavet空间的R指数特征

The Relationship Between R Index and Daugavet Property

揭示了具有Daugavet性质的Banach空间所具有的R指数特征;证明了R指数ε(X)=2是X具有Daugavet性质的必要条件;如果ε(X)=2,则X包含一个与l1同构的子空间;如果ε(X)=2,则X包不是自反空间.

Daugavet index was introduced to reflect Daugavet property of Banach space.The main conclusions can be summarized to some items as follows:if space X has Daugavet property,then R indexε(X)=2;ifε(X)=2,then X contains a subspace isomorphic to l1;ifε(X)=2,then X is not reflexive.