Geodesic
Complemented subspaces with a strong finite-dimensional decomposition of nuclear Köthe spaces have a basis
Studia Mathematica, Tome 127 (1998) no. 1, pp. 1-7
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The following result is proved: Let E be a complemented subspace with an r-finite-dimensional decomposition of a nuclear Köthe space λ(A). Then E has a basis. 
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Jörg Krone; Volker Walldorf. Complemented subspaces with a strong finite-dimensional decomposition of nuclear Köthe spaces have a basis. Studia Mathematica, Tome 127 (1998) no. 1, pp. 1-7. doi: 10.4064/sm-127-1-1-7

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