Mapping Properties of $c_0$

Lewis, Paul

Mapping Properties of

c_{0}

Lewis, Paul

Colloquium Mathematicae, Tome 79 (1999), p. 235-244 / Harvested from The Polish Digital Mathematics Library

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Résumé

Bessaga and Pełczyński showed that if $c_{0}$ embeds in the dual $X^{*}$ of a Banach space X, then $ℓ^{1}$ embeds as a complemented subspace of X. Pełczyński proved that every infinite-dimensional closed linear subspace of $ℓ^{1}$ contains a copy of $ℓ^{1}$ that is complemented in $ℓ^{1}$ . Later, Kadec and Pełczyński proved that every non-reflexive closed linear subspace of $L^{1} [0, 1]$ contains a copy of $ℓ^{1}$ that is complemented in $L^{1} [0, 1]$ . In this note a traditional sliding hump argument is used to establish a simple mapping property of $c_{0}$ which simultaneously yields extensions of the preceding theorems as corollaries. Additional classical mapping properties of $c_{0}$ are briefly discussed and applications are given.

Publié le : 1999-01-01

Zbl 0942.46015

EUDML-ID : urn:eudml:doc:210714

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     author = {Paul Lewis},
     title = {Mapping Properties of $c\_0$
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     journal = {Colloquium Mathematicae},
     volume = {79},
     year = {1999},
     pages = {235-244},
     zbl = {0942.46015},
     language = {en},
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Lewis, Paul. Mapping Properties of $c_0$
            . Colloquium Mathematicae, Tome 79 (1999) pp. 235-244. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv80i2p235bwm/

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