A splitting theory for the space of distributions

被引：28
|
作者：
Domanski, P
Vogt, D
机构：
[1] Polish Acad Sci, Math Inst, Poznan Branch, PL-60769 Poznan, Poland
[2] Berg Univ Gesamthsch Wuppertal, D-42097 Wuppertal, Germany
来源：
STUDIA MATHEMATICA | 2000年 / 140卷 / 01期
关键词：
exact complex; systems of partial differential equations; short exact sequence; splitting; space of distributions; lifting of Banach discs; Schwartz spaces; nuclear spaces; ultrabornological associated space; omega;
D O I：
10.4064/sm-140-1-57-77
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The splitting problem is studied for short exact sequences consisting of countable projective limits of DFN-spaces (*) 0 --> F --> X --> G --> 0, where F or G are isomorphic to the space of distributions D'. It is proved that every sequence (*) splits for F similar or equal to D' iff G is a subspace of D' and that, for ultrabornological F, every sequence (*) splits for G similar or equal to D' iff F is a quotient of D'.
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页码：57 / 77
页数：21
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