Geodesic
On some generalizations of bases in Banach spaces
Sbornik. Mathematics, Tome 49 (1984) no. 1, pp. 269-281 Cet article a éte moissonné depuis la source Math-Net.Ru

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This article considers pseudobases and quasibases in Banach spaces, as introduced by Gelbaum. A geometric characterization of pseudobases is established. It is proved that pseudobases are stable. It is shown that pseudobases and quasibases in the $L^p$-spaces do not, in general, have an interpolation property with respect to these spaces which is inherent to bases. Namely, an example is constructed of a system of functions that is an unconditional quasibasis in $L^2(0,\,1)$ and $L^q(0,\,1)$ ($q\in(1,\,2)$ fixed) and at the same time is not a pseudobasis in any $L^p(0,\,1)$ with $p\in(q,\,2)$ for any rearrangement of it. Bibliography: 10 titles. 
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A. N. Slepchenko. On some generalizations of bases in Banach spaces. Sbornik. Mathematics, Tome 49 (1984) no. 1, pp. 269-281. http://geodesic.mathdoc.fr/item/SM_1984_49_1_a16/

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