摘要
本文证明了Banach格E的一个正规化基{x_n}是格等价于l_1的自然基{e_n}的充要条件是每一Banach格F到E内的正紧算子T都有形如 Tx=∑<x,a_n>x_n的表达式,其中∑a_n是F’中w~*-无条件收敛级数,且a_n≥0。一些相关的结果也略加讨论。
Proves that a normalized basis {x_n}(?)E of a Banach lattice E is lattice equivalent to the natural basis {e_n} of 1_1 if and only if every positive compact operator T from a Banach lattice F into E has a representation of form Tx=∑<x, α_n>x_n, where ∑α_n is a w~*-unconditionally convergent series in F' and α_n≥0. Some related results are discussed.
出处
《西南交通大学学报》
EI
CSCD
北大核心
1989年第1期112-118,共7页
Journal of Southwest Jiaotong University
关键词
格
基
正紧算子
格等价
空间l_1
lattice
basis
positive compact operator
lattice equivalence
space 1_1
