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arXiv · 1003.5708

Direct sums and the Szlenk index

Philip A. H. Brooker
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Abstract

For $α$ an ordinal and $1<p<\infty$, we determine a necessary and sufficient condition for an $\ell_p$-direct sum of operators to have Szlenk index not exceeding $ω^α$. It follows from our results that the Szlenk index of an $\ell_p$-direct sum of operators is determined in a natural way by the behaviour of the $ε$-Szlenk indices of its summands. Our methods give similar results for $c_0$-direct sums.

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BibTeXRIS

Philip A. H. Brooker. 2010-09-10. Direct sums and the Szlenk index. https://doi.org/10.1016/j.jfa.2010.12.016

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