Geodesic
Bari bases of subspaces
Matematičeskie zametki, Tome 5 (1969) no. 4, pp. 461-469.

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We shall establish certain characteristic properties of Bari bases of subspaces. We shall show that a complete sequence of finite-dimensional subspaces $\{\mathfrak{R}_j\}_1^\infty$ is a Bari basis if and only if each sequence $\{\psi_j\}_1^\infty$ ($\psi_j\in\mathfrak{R}_j$, $||\psi_j||=1$) is a Bari basis of its own closed linear hull. 
@article{MZM_1969_5_4_a9,
     author = {A. S. Markus},
     title = {Bari bases of subspaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {461--469},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {1969},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_4_a9/}
}
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A. S. Markus. Bari bases of subspaces. Matematičeskie zametki, Tome 5 (1969) no. 4, pp. 461-469. http://geodesic.mathdoc.fr/item/MZM_1969_5_4_a9/