On operators from separable reflexive spaces with asymptotic structure
نویسندگان
چکیده
Let 1 < q < p < ∞ and q ≤ r ≤ p. Let X be a reflexive Banach space satisfying a lower-lq-tree estimate and let T be a bounded linear operator from X which satisfies an upper-lp-tree estimate. Then T factors through a subspace of ( ∑ Fn)lr , where (Fn) is a sequence of finite-dimensional spaces. In particular, T factors through a subspace of a reflexive space with an (lp, lq) FDD. Similarly, let 1 < q < r < p < ∞ and let X be a separable reflexive Banach space satisfying an asymptotic lower-lq-tree estimate. Let T be a bounded linear operator from X which satisfies an asymptotic upper-lp-tree estimate. Then T factors through a subspace of ( ∑ Gn)lr , where (Gn) is a sequence of finite-dimensional spaces. In particular, T factors through a subspace of a reflexive space with an asymptotic (lp, lq) FDD.
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