On the splitting relation for fréchet-hilbert spaces

Abstract

A shorter proof is given for a theorem of Domanski and Mastyło characterizing the pairs (E; F) of Fréchet-Hilbert spaces with the property that every exact sequence 0 → F → G → E → 0 of Fréchet-Hilbert spaces splits. The results on acyclicity of inductive spectra of metrizable locally convex spaces which we use are also presented with proofs.