Ideals of subseries convergence and F-spaces
Ideals of subseries convergence and F-spaces
复制标题
DOI：
10.1007/s00013-016-0966-3
复制
发表时间：
2017
影响因子：
0.6
通讯作者：
L. Drewnowski;I. Labuda
中科院分区：
文献类型：
--
作者：
L. Drewnowski;I. Labuda
设X是ANF-空间，是INX的一个向量序列。考虑了子级数收敛的理想。特别地，我们证明了利用理想得到的不含C0的Banach空间类的一个刻画在每一个不同构于Banach空间的Fréchet空间中都失效了。另一方面，通过定义满足Orlicz条件(O)的一类新的F-空间，可以将结果推广到某些F-空间。关于与F-SpaceX相关的所有理想族，得到了一个区分有限维和无限维情形的定理。
LetXbe anF-space andbe a sequence of vectors inX. Idealsof subseries convergence are considered. In particular, we show that a characterization of the class of Banach spaces not containingc0obtained by using the idealsbreaks down in every Fréchet space not isomorphic to a Banach space. On the other hand, the result can be extended to someF-spaces via the definition of a new class ofF-spaces satisfying a stronger version of the condition (O) of Orlicz. A theorem discriminating between the finite and infinite dimensional case is obtained about the familyof all ideals associated with theF-spaceX.