Geodesic
On the Classification of Biorthogonal Sequences
Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 721-733

Voir la notice de l'article provenant de la source Cambridge University Press

The work of various authors (e.g. Frink [3] and Markushevitch [7]) suggests the possibility of studying complete biorthogonal sequences in Banach spaces as a generalization of orthogonal families of continuous functions. But except for the case where the complete biorthogonal sequence is a Schauder basis such studies have not led to a very rich theory. The main reason for this is that an arbitrary complete biorthogonal sequence is not likely to have many helpful properties. For instance, in every separable Banach space X one can find a complete biorthogonal sequence {ei , Ei } which is not one-summable. 
Ruckle, William H. On the Classification of Biorthogonal Sequences. Canadian journal of mathematics, Tome 26 (1974) no. 3, pp. 721-733. doi: 10.4153/CJM-1974-067-0
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