## On the splitting relation for Fréchet-Hilbert spaces.(English)Zbl 1230.46005

The splitting problem for exact sequences of locally convex spaces consists in characterizing those pairs $$(E,F)$$ of locally convex spaces for which every short exact sequence $$0\rightarrow F\rightarrow G\rightarrow E \rightarrow 0$$ splits. For pairs $$(E,F)$$ of Fréchet-Hilbert spaces, this was solved by P. Domański and M. Mastyło, [“Characterization of splitting for Fréchet–Hilbert spaces via interpolation”, Math. Ann. 339, No. 2, 317–340 (2007; Zbl 1132.46043)]. In the present paper, a short elegant proof of this result is presented, including a new formulation and the proof of the crucial interpolation theorem from [loc. cit.] and full proofs of the results on acyclicity of inductive spectra, as far as they are needed in the difficult sufficiency part of the characterization.

### MSC:

 46A04 Locally convex Fréchet spaces and (DF)-spaces 46M18 Homological methods in functional analysis (exact sequences, right inverses, lifting, etc.) 46M40 Inductive and projective limits in functional analysis 46A63 Topological invariants ((DN), ($$\Omega$$), etc.) for locally convex spaces 46B70 Interpolation between normed linear spaces

Zbl 1132.46043
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### References:

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