空间的几种超投影性质及其局部化

Some Superprojective Properties of Banach Spaces and Their Localizations

中文关键词:  l_p-超投影空间  强超投影空间  局部l_p-超投影空间  局部强超投影空间  超投影空间  局部超投影空间

英文关键词:l_p-superprojective space  strong superprojective space  local l_p-superprojective space  local strong superprojective space  superprojective space  local subprojective space

中文摘要:

      讨论Banach空间几种超投影性质(及其相应的局部化性质)之间的关系,证明了在Banach空间X自反的条件下,X是l_p-次投影空间的充要条件是X^*是l_p-超投影空间,X是局部l_p-次投影空间的充要条件是X^*是局部l_p-超投影空间,以及X是局部次投影空间的充要条件是X^*是局部超投影的。其中1/p+1/q=1(p>1,q>1)。

英文摘要:

      In this article the relations between superprojective properties and local superpro- jective propcrtics of Banach space are discussed. For a reflexivc Banach space X, it is proved that X is l_p-subprojective space if and only if X^* is l_p-superprojective space, X is local l_p-sub- projective spacc if and only if X^* is local l_p-superprojective space and X is local subprojective space if and only if X^* is local superprojective space, where 1/p+1/q=1.