Abstract
Based on the methods from interpolation theory we give a characterization of pairs (E, F) of Fréchet-Hilbert spaces so that for each Fréchet–Hilbert space G each short exact sequence \(0 \rightarrow F \rightarrow G \rightarrow E \rightarrow 0\) splits. This characterization essentially depends on a key condition (S) of an interpolation nature. An equivalent description of (S) in terms of appropriate families of interpolation functions for Fré spaces is presented. We also define and study general variants of interpolation type of some well known linear topological invariants. As an application we obtain an extension of the well known (DN)–(Ω) splitting theorem of Vogt.
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The work of the first author was supported by Committee of Scientific Research (KBN), Poland, grant P03A 022 25. The work of the second author was supported by Committee of Scientific Research (KBN), Poland, grant P03A 013 26.
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Domański, P., Mastyło, M. Characterization of splitting for Fréchet–Hilbert spaces via interpolation. Math. Ann. 339, 317–340 (2007). https://doi.org/10.1007/s00208-007-0115-1
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DOI: https://doi.org/10.1007/s00208-007-0115-1