Direct sums and the Szlenk index

Philip A.H. Brooker

doi:10.1016/j.jfa.2010.12.016

Direct sums and the Szlenk index

Philip A.H. Brooker^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

For α an ordinal and 1<p<∞, we determine a necessary and sufficient condition for an ℓp-direct sum of operators to have Szlenk index not exceeding ω^α. It follows from our results that the Szlenk index of an ℓp-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 c0-direct sums.

Original language	English
Pages (from-to)	2222-2246
Number of pages	25
Journal	Journal of Functional Analysis
Volume	260
Issue number	8
DOIs	https://doi.org/10.1016/j.jfa.2010.12.016
Publication status	Published - 15 Apr 2011

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10.1016/j.jfa.2010.12.016

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title = "Direct sums and the Szlenk index",

abstract = "For α an ordinal and 1α. It follows from our results that the Szlenk index of an ℓp-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 c0-direct sums.",

keywords = "Asplund operators, Banach spaces, Direct sums, Szlenk index",

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AB - For α an ordinal and 1α. It follows from our results that the Szlenk index of an ℓp-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 c0-direct sums.

KW - Asplund operators

KW - Banach spaces

KW - Direct sums

KW - Szlenk index

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DO - 10.1016/j.jfa.2010.12.016

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JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

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Direct sums and the Szlenk index

Abstract

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