Independent sequences in Banach spaces

descriptionPublicationkeyboard_double_arrow_right Article 01 Jun 1982 English Publisher:Springer Science and Business Media LLCJournal:Israel Journal of Mathematics, volume 41, pages 147-150 (issn: 0021-2172, eissn: 1565-8511,

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Authors: Szankowski, A.; Terenzi, P.;

doi: 10.1007/bf02760661

Independent sequences in Banach spaces

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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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Keywords

fundamental linearly independent sequence, Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces, omega-independent subsequence

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