关于巴拿赫格中的$l^\infty$渐进等距拷贝

Asymptotically Isometric Copies of $l^\infty$ in Some Banach Lattices

中文关键词:  渐进等距拷贝  巴拿赫格  Fenchel-Orlicz空间.

英文关键词:asymptotically isometric copy  Banach lattice  Fenchel-Orlicz space.

中文摘要:

      本文证明了具有$\sigma$-序半连续但非$\sigma$-序连续范数的$\sigma$-完备巴拿赫格包含$l^\infty$的渐进等距拷贝.并且证明了具有Orlicz范数的Fenchel-Orlicz空间不一定含有$l^\infty$的渐进等距拷贝.

英文摘要:

      In this paper, we show that any $\sigma$-complete Banach lattice, with a $\sigma$-order semi-continuous but not $\sigma$-order continuous norm, contains an asymptotically isometric copy of $l^\infty$. We also get that the Fenchel-Orlicz space with the Orlicz norm may not contain an asymptotically isometric copy of $l^\infty$.