A splitting theory for the space of distributions
Volume 140 / 2000
Studia Mathematica 140 (2000), 57-77
DOI: 10.4064/sm-140-1-57-77
Abstract
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 ≃ D' iff G is a subspace of D' and that, for ultrabornological F, every sequence (*) splits for G ≃ D' iff F is a quotient of D'
