Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4673291 | Indagationes Mathematicae | 2007 | 18 Pages |
Abstract
Let X be a Banach space, let Y be its subspace, and let Г be an infinite set. We study the consequences of the assumption that an operator T embeds ℓ221E;(Г) into X isomorphically with T(c0(Г)) ⊂ Y. Under additional assumptions on T we prove the existence of isomorphic copies of c0(Гℵ0) in X/Y, and complemented copies ℓ∞(Г) in X/Y. In concrete cases we obtain a new information about the structure of X/Y. In particular, L∞[O,1]/C[O,1] contains a complemented copy of ℓ∞/c0, and some natural (lattice) quotients of real Orlicz and Marcinkiewicz spaces contain lattice-isometric and positively I-complemented copies of(real) ℓ∞/c0.
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