On the existence of basic sequences in non-archimedean locally convex spaces
Śliwa, Wiesław
Bull. Belg. Math. Soc. Simon Stevin, Tome 12 (2006) no. 5, p. 363-372 / Harvested from Project Euclid
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We prove that there exist non-archimedean (n.a.) locally convex spaces without basic orthogonal sequences, and even without Schauder basic sequences. Among other things any n.a. Köthe space with the weak topology has no basic orthogonal sequence. On the other hand, we show that the strong dual of any infinite-dimensional n.a. polar Fréchet space and any n.a. LF-space have basic orthogonal sequences.
Publié le : 2006-06-14
Classification:  Orthogonal basic sequence,  Schauder basic sequence,  46S10,  46A35 
@article{1148059471,
     author = {\'Sliwa, Wies\l aw},
     title = {On the existence of basic
sequences in non-archimedean locally convex spaces},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {12},
     number = {5},
     year = {2006},
     pages = { 363-372},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1148059471}
}

Śliwa, Wiesław. On the existence of basic
sequences in non-archimedean locally convex spaces. Bull. Belg. Math. Soc. Simon Stevin, Tome 12 (2006) no. 5, pp.  363-372. http://gdmltest.u-ga.fr/item/1148059471/