Abstract
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.
Publisher
Canadian Mathematical Society
Cited by
8 articles.
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1. General criteria for a stronger notion of lineability;Proceedings of the American Mathematical Society;2024-01-11
2. On a semigroup problem;Discrete & Continuous Dynamical Systems - S;2019
3. On the work of Lech Drewnowski;Functiones et Approximatio Commentarii Mathematici;2014-03-01
4. Remarks and examples concerning the weak basis theorem;Archiv der Mathematik;1991-04
5. On basis sequences in non-locally convex spaces;Studia Mathematica;1980