Transactions of the American Mathematical Society

Author(s): Ioannis Gasparis
Journal: Trans. Amer. Math. Soc. 357 (2005), 1-30.
MSC (2000): Primary 46B03; Secondary 06A07, 03E02
Posted: August 19, 2004
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Abstract: It is proved that an operator $T \colon C(K) \to X$ , $K$ compact metrizable, $X$ a separable Banach space, for which the $\epsilon$ -Szlenk index of $T^*(B_{X^*})$ is greater than or equal to $\omega^\xi$ , $\xi < \omega_1$ , is an isomorphism on a subspace of $C(K)$ isomorphic to $X_\xi$ , the Schreier space of order $\xi$ . As a corollary, one obtains that a complemented subspace of $C(K)$ with Szlenk index equal to $\omega^{\xi + 1}$ contains a subspace isomorphic to $X_\xi$ .

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 46B03, 06A07, 03E02

Ioannis Gasparis
Affiliation: Department of Mathematics, University of Crete, Knossou Avenue, P.O. Box 2208, Heracleion 71409, Greece
Address at time of publication: Department of Mathematics, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece
Email: ioagaspa@math.uoc.gr, iogaspa@auth.gr

DOI: 10.1090/S0002-9947-04-03688-8
PII: S 0002-9947(04)03688-8
Keywords: $C(K)$ space, Szlenk index, projection, Schreier sets
Received by editor(s): February 4, 2003
Posted: August 19, 2004
Copyright of article: Copyright 2004, American Mathematical Society

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