Geodesic
Block sequences in nuclear Fr\'echet spaces with basis
Matematičeskie zametki, Tome 17 (1975) no. 6, pp. 899-908

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It is shown that a block sequence in a nuclear Fréchet space with a basis has a block extension if and only if the subspace it generates is complemented. In addition, a short proof is given of the following result of Dubinsky and Robinson: a nuclear Fréchet space is isomorphic to $\omega=R^N$, $N=\{1,2,\dots\}$ if it has a basis such that any block sequence with blocks of length $\le2$ of any permutation of this basis has a block extension. It is shown that a similar result holds without considering permutations of the basis if the length of the blocks is arbitrary. 
@article{MZM_1975_17_6_a7,
     author = {P. B. Djakov},
     title = {Block sequences in nuclear {Fr\'echet} spaces with basis},
     journal = {Matemati\v{c}eskie zametki},
     pages = {899--908},
     publisher = {mathdoc},
     volume = {17},
     number = {6},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a7/}
}
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P. B. Djakov. Block sequences in nuclear Fr\'echet spaces with basis. Matematičeskie zametki, Tome 17 (1975) no. 6, pp. 899-908. http://geodesic.mathdoc.fr/item/MZM_1975_17_6_a7/