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

Access to Document

10.1016/j.jfa.2010.12.016

Cite this

@article{1b8363e54e5c47c4b61b32304d5866bb,

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",

author = "Brooker, \{Philip A.H.\}",

year = "2011",

month = apr,

day = "15",

doi = "10.1016/j.jfa.2010.12.016",

language = "English",

volume = "260",

pages = "2222--2246",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "8",

}

TY - JOUR

T1 - Direct sums and the Szlenk index

AU - Brooker, Philip A.H.

PY - 2011/4/15

Y1 - 2011/4/15

N2 - 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.

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

UR - https://www.scopus.com/pages/publications/79551492521

U2 - 10.1016/j.jfa.2010.12.016

DO - 10.1016/j.jfa.2010.12.016

M3 - Article

SN - 0022-1236

VL - 260

SP - 2222

EP - 2246

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 8

ER -

Direct sums and the Szlenk index

Abstract

Access to Document

Other files and links

Fingerprint

Cite this