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- W4300715189 abstract "Let $X$ be a Banach space with an unconditional finite-dimensional Schauder decomposition $(E_n)$. We consider the general problem of characterizing conditions under which one can construct an unconditional basis for $X$ by forming an unconditional basis for each $E_n.$ For example, we show that if $sup dim E_n<infty$ and $X$ has Gordon-Lewis local unconditional structure then $X$ has an unconditional basis of this type. We also give an example of a non-Hilbertian space $X$ with the property that whenever $Y$ is a closed subspace of $X$ with a UFDD $(E_n)$ such that $supdim E_n<infty$ then $Y$ has an unconditional basis, showing that a recent result of Komorowski and Tomczak-Jaegermann cannot be improved." @default.
- W4300715189 created "2022-10-04" @default.
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- W4300715189 date "1994-08-24" @default.
- W4300715189 modified "2023-10-18" @default.
- W4300715189 title "Unconditional bases and unconditional finite-dimensional decompositions in Banach spaces" @default.
- W4300715189 doi "https://doi.org/10.48550/arxiv.math/9408207" @default.
- W4300715189 hasPublicationYear "1994" @default.
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