Geodesic
On the Weak Basis Theorem in F-spaces
Canadian journal of mathematics, Tome 26 (1974) no. 6, pp. 1294-1300

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

It is well-known that every weak basis in a Fréchet space is actually a basis. This result, called the weak basis theorem was first given for Banach spaces in 1932 by Banach [1, p. 238], and extended to Fréchet spaces by Bessaga and Petczynski [3]. McArthur [12] proved an analogue for bases of subspaces in Fréchet spaces, and recently W. J. Stiles [18, Corollary 4.5, p. 413] showed that the theorem fails in the non-locally convex spaces lp (0 < p < 1). The purpose of this paper is to prove the following generalization of Stiles' result. 
Shapiro, Joel H. On the Weak Basis Theorem in F-spaces. Canadian journal of mathematics, Tome 26 (1974) no. 6, pp. 1294-1300. doi: 10.4153/CJM-1974-124-5
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