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Subseries convergence in spaces with a Schauder basis


Author: Charles Swartz
Journal: Proc. Amer. Math. Soc. 123 (1995), 455-457
MSC: Primary 46A35; Secondary 40J05
DOI: https://doi.org/10.1090/S0002-9939-1995-1216826-9
MathSciNet review: 1216826
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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 \in {\mathbf{N}}\} $. We show that if a series in E is subseries convergent with respect to $ \sigma (E,F)$, then it is subseries convergent with respect to the original topology of E.


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DOI: https://doi.org/10.1090/S0002-9939-1995-1216826-9
Article copyright: © Copyright 1995 American Mathematical Society

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