Copies of c0(Г) and ?∞(Г)/c0(Г) in quotients of Banach spaces with applications to Orlicz and Marcinkiewicz spaces |
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Authors: | Anatolij Plichko |
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Affiliation: | a Instytut Matematyki, Politechnika Krakowska, ul. Warszawska 24, 31-155 Kraków, Poland b Instytut Matematyki, Uniwersytet Kazimierza Wielkiego, Pl. Wevssenhoffa 11, 85-072 Bydgoszcz, Poland |
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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 ?221E;(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 ?∞(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 ?∞/c0, and some natural (lattice) quotients of real Orlicz and Marcinkiewicz spaces contain lattice-isometric and positively I-complemented copies of(real) ?∞/c0. |
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Keywords: | Primary, 46B25 secondary, 46B26, 46B42 |
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