On strongly asymptotic lp spaces and minimality

S. J. Dilworth; V. Ferenczi; Kutzarova Denka; E. Odell

doi:10.1112/jlms/jdm003

On strongly asymptotic l_p spaces and minimality

S. J. Dilworth, V. Ferenczi, Kutzarova Denka, E. Odell

Mathematics

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

Abstract

Let 1 ≤ p ≤ ∞ and let X be a Banach space with a semi-normalized strongly asymptotic l_p basis (e,;). If X is minimal and 1 ≤ p < 2, then X is isomorphic to a subspace of l_p. If X is minimal and 2 ≤ p < ∞, or if X is complementably minimal and 1 ≤ p ≤ ∞, then (e_i) is equivalent to the unit vector basis of l_p (or C_O if p = ∞).

Original language	English (US)
Pages (from-to)	409-419
Number of pages	11
Journal	Journal of the London Mathematical Society
Volume	75
Issue number	2
DOIs	https://doi.org/10.1112/jlms/jdm003
State	Published - Apr 2007

ASJC Scopus subject areas

General Mathematics

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title = "On strongly asymptotic lp spaces and minimality",

abstract = "Let 1 ≤ p ≤ ∞ and let X be a Banach space with a semi-normalized strongly asymptotic lp basis (e,;). If X is minimal and 1 ≤ p < 2, then X is isomorphic to a subspace of lp. If X is minimal and 2 ≤ p < ∞, or if X is complementably minimal and 1 ≤ p ≤ ∞, then (ei) is equivalent to the unit vector basis of lp (or CO if p = ∞).",

author = "Dilworth, {S. J.} and V. Ferenczi and Kutzarova Denka and E. Odell",

note = "Funding Information: The first, third, and fourth authors were supported by the Workshop in Analysis and Probability at Texas A&M University in 2005. Research of the fourth author was partially supported by the National Science Foundation.",

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AU - Dilworth, S. J.

AU - Ferenczi, V.

AU - Denka, Kutzarova

AU - Odell, E.

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