A shorter proof is given for a theorem of Domański and Mastyło characterizing the pairs $(E,F)$ of Frèchet-Hilbert spaces with the property that every exact sequence $0\to F\to G\to E\to 0$ of Frèchet-Hilbert spaces splits. The results on acyclicity of inductive spectra of metrizable locally convex spaces which we use are also presented with proofs.
"On the splitting relation for Frèchet-Hilbert spaces." Funct. Approx. Comment. Math. 44 (2) 215 - 225, June 2011. https://doi.org/10.7169/facm/1308749125