Subspaces and quotients of Banach spaces with shrinking unconditional bases |
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Authors: | W B Johnson Bentuo Zheng |
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Institution: | 1.Department of Mathematics,Texas A&M University,College Station,USA;2.Department of Mathematics,The University of Texas at Austin,Austin,USA;3.Department of Mathematical Sciences,The University of Memphis,Memphis,USA |
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Abstract: | The main result is that a separable Banach space with the weak* unconditional tree property is isomorphic to a subspace as
well as a quotient of a Banach space with a shrinking unconditional basis. A consequence of this is that a Banach space is
isomorphic to a subspace of a space with a shrinking unconditional basis if and only if it is isomorphic to a quotient of
a space with a shrinking unconditional basis, which solves a problem dating to the 1970s. The proof of the main result also
yields that a uniformly convex space with the unconditional tree property is isomorphic to a subspace as well as a quotient
of a uniformly convex space with an unconditional finite dimensional decomposition. |
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Keywords: | |
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