Abstract
In every ∞-dimensional separable Banach spaceX there is a fundamental sequence such that no subsequence of it, which is fundamental inX, is independent (“{x n} is fundamental inX” meansX=span {x n}).
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References
P. Erdös and E. G. Straus,On linear independence of sequences in a Banach space, Pacific J. Math.3 (1953), 689–694.
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Szankowski, A., Terenzi, P. Independent sequences in Banach spaces. Israel J. Math. 41, 147–150 (1982). https://doi.org/10.1007/BF02760661
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DOI: https://doi.org/10.1007/BF02760661