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arXiv · 2105.12289

On a characterization of convergence in Banach spaces with a Schauder basis

Marat V. Markin·Olivia B. Soghomonian
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Abstract

We extend the well-known characterizations of convergence in the spaces $l_p$ ($1\le p<\infty$) of $p$-summable sequence and $c_0$ of vanishing sequences to a general characterization of convergence in a Banach space with a Schauder basis and obtain as instant corollaries characterizations of convergence in an infinite-dimensional separable Hilbert space and the space $c$ of convergent sequences.

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Marat V. Markin, Olivia B. Soghomonian. 2021-05-26. On a characterization of convergence in Banach spaces with a Schauder basis. https://doi.org/10.1155/2021%2F1640183

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