Extension and splitting theorems for Fréchet spaces of type 2 (Q1974102)

It is well-known theorem of \textit{B. Maurey} [C. R. Acad. Sci., Paris, Sér. A 279, 329-332 (1974; Zbl 0291.47001)]: each operator from a subspace \(E\) of a Banach space \(G\) of type 2 into a Banach space of cotype 2 extends to the whole space \(G\). In the Fréchet space case even a subspace of a hilbertizable space (i.e., a projective limit of Hilbert spaces) could be uncomplemented. Thus there is no straightforward generalization of Maurey's result. On the other hand, for hilbertizable spaces the splitting result of \textit{D. Vogt} [``Interpolation of nuclear operators and a splitting theorem for exact sequences of Fréchet spaces'', preprint] holds: a closed subspace \(F\) of a hilbertizable Frechet space \(G\) such that \(F\) has property \dots{} and \(G/F\) has property \((DN)\), is complemented. In this paper it is proved that a hilbertizable Fréchet subspace \(F\) of a Fréchet space \(G\) of type 2 (i.e., a projective limit of type 2 Banach spaces) is complemented whenever \(F\) and \(G/F\) satisfy Vogt's conditions.