Subspaces containing biorthogonal functionals of bases of different types

Details Subspaces containing biorthogonal functionals of bases of different types Subspaces containing biorthogonal functionals of bases of different types

1994-04-20

arxiv.org/abs/math/9404213v1

Teor. Funktsii, Funktsional. Anal. i Prilozhen. 57 (1992), 115-127; English transl.: J. Math. Sci., 77 (1995), no. 1, 3008-301

Mathematics

Functional Analysis

Scientific paper

The paper is devoted to two particular cases of the following general problem. Let $\alpha$ and $\beta$ be two types of bases in Banach spaces. Let a Banach space $X$ has bases of both types and a subspace $M\subset X^*$ contains the sequence of biorthogonal functionals of some $\alpha$-basis in $X$. Does $M$ contain a sequence of biorthogonal functionals of some $\beta$-basis in $X$? The following particular cases are considered: $(\alpha, \beta)$=(Schauder bases, unconditional bases), $(\alpha, \beta)$=(Nonlinear operational bases, linear operational bases). The paper contains an investigation of some of the spaces constructed by S.Belle\-not in ``The $J$-sum of Banach spaces'', J. Funct. Anal. {\bf 48} (1982), 95--106. (These spaces are used in some examples.)

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