SUBSERIES CONVERGENCE IN SPACES WITH A SCHAUDER BASIS

Authors
SWARTZ C
Citation
C. Swartz, SUBSERIES CONVERGENCE IN SPACES WITH A SCHAUDER BASIS, Proceedings of the American Mathematical Society, 123(2), 1995, pp. 455-457
Citations number
8
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
123
Issue
2
Year of publication
1995
Pages
455 - 457
Database
ISI
SICI code
0002-9939(1995)123:2<455:SCISWA>2.0.ZU;2-O
Abstract
Let E be a Hausdorff topological vector space having a Schauder basis {b(i)} and coordinate functionals {f(i)}. Let sigma(E, F) be the weak topology on E induced by F = {f(i): i is an element of N}. We show tha t if a series in E is subseries convergent with respect to sigma(E, F) , then it is subseries convergent with respect to the original topolog y of E.