Operators on $C(K)$ spaces preserving copies of Schreier spaces
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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 $X_\xi$.References
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Additional Information
- 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
- Received by editor(s): February 4, 2003
- Published electronically: August 19, 2004
- © Copyright 2004 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 357 (2005), 1-30
- MSC (2000): Primary 46B03; Secondary 06A07, 03E02
- DOI: https://doi.org/10.1090/S0002-9947-04-03688-8
- MathSciNet review: 2098084