关于 ``Banach spaces failing the almost isometric universal extension property'' 的一个注记

A Note of Paper ``Banach Spaces Failing the Almost Isometric Universal Extension Property"

中文关键词:  有常数$\alpha$的性质${\cal A}$  凸性模  $\lambda$-EP  $\lambda$-UEP.

英文关键词:property ${\cal A}$ with constant $\alpha$  modulus of convexity  $\lambda$-EP  $\lambda$-UEP.

中文摘要:

      D.M. Speegle 在文献[1] 中给出了具有常数 $\alpha$的性质${\cal A}$ 的定义,并且证明了任意无限维的可分一致光滑Banach空间都具有这样的性质,而且常数 $\alpha\in [0,1)$.本文给出了一个使得无限维可分Banach空间具有这种性质的充分条件,以及几个关于文献[1] 的注解.

英文摘要:

      The definition of property ${\cal A}$ with constant $\alpha$ was introduced by D. M. Speegle, who proved that every infinite dimensional separable uniformly smooth Banach space has property ${\cal A}$ with constant $\alpha \in[0,1)$. In this paper, we give a sufficient condition for a Banach space to have property ${\cal A}$ with constant $\alpha \in[0,1)$, and some remarks on Speegle's paper [1].