A ug 1 99 4 UNCONDITIONAL BASES AND UNCONDITIONAL FINITE - DIMENSIONAL DECOMPOSITIONS IN BANACH SPACES
نویسندگان
چکیده
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 < ∞ 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 sup dim E n < ∞ then Y has an unconditional basis, showing that a recent result of Komorowski and Tomczak-Jaegermann cannot be improved.
منابع مشابه
Unconditional Bases and Unconditional Finite-dimensional Decompositions in Banach Spaces
Let X he a Banach space with an unconditional finite-dimensional Schauder decomposition (En). 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 En. For example, we show that if sup,, dim En < c~ and X has Gordon-Lewis local unconditional s t ructure then X has an unconditional basis ...
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