The Szlenk index and local l_1-indices

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dc.creatorAlspach, Dale
dc.creatorJudd, Robert
dc.creatorOdell, Edward
dc.date2000-09-29
dc.date.accessioned2026-07-07T04:37:44Z
dc.date.available2026-07-07T04:37:44Z
dc.descriptionWe introduce two new local l_1-indices of the same type as the Bourgain l_1 index; the l_1^+-index and the l_1^+-weakly null index. We show that the l_1^+-weakly null index of a Banach space X is the same as the Szlenk index of X, provided X does not contain l_1. The l_1^+-weakly null index has the same form as the Bourgain l_1 index: if it is countable it must take values omega^alpha for some alpha<omega_1. The different l_1-indices are closely related and so knowing the Szlenk index of a Banach space helps us calculate its local l_1-index, via the l_1^+-weakly null index. We show that I(C(omega^{omega^alpha}))=omega^{1+alpha+1}.
dc.descriptionLaTeX2e, 41 pages, to appear in Positivity
dc.identifierhttps://arxiv.org/abs/math/0009250
dc.identifierhttp://arxiv.org/abs/math/0009250
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/60015
dc.subjectFunctional Analysis
dc.subject46B
dc.titleThe Szlenk index and local l_1-indices
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