Geodesic
On the existence of a~basis in a~complemented subspace of a~nuclear K\"othe space from class~$(d_1)$
Sbornik. Mathematics, Tome 209 (2018) no. 10, pp. 1463-1481

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A proof is presented that an arbitrary complemented subspace of a Köthe nuclear space from class $(d_1)$ has a basis, provided that the relevant Köthe matrix is regular in the sense of Dragilev. It is also shown that each such subspace must have a basis that is quasi-equivalent to a part of the canonical unit-vector basis. Bibliography: 21 titles.
Keywords: basis, Köthe nuclear spaces, complemented subspaces.
Mots-clés : Pelczyński's conjecture 
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     title = {On the existence of a~basis in a~complemented subspace of a~nuclear {K\"othe} space from class~$(d_1)$},
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A. K. Dronov; V. M. Kaplitskii. On the existence of a~basis in a~complemented subspace of a~nuclear K\"othe space from class~$(d_1)$. Sbornik. Mathematics, Tome 209 (2018) no. 10, pp. 1463-1481. http://geodesic.mathdoc.fr/item/SM_2018_209_10_a2/