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On strongly asymptotic l p spaces and minimality
Author(s) -
Dilworth S. J.,
Ferenczi V.,
Kutzarova Denka,
Odell E.
Publication year - 2007
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm003
Subject(s) - banach space , mathematics , subspace topology , basis (linear algebra) , unit (ring theory) , combinatorics , space (punctuation) , unit vector , pure mathematics , mathematical analysis , geometry , computer science , mathematics education , operating system
Let 1 ⩽ p ⩽ ∞ and let X be a Banach space with a semi‐normalized strongly asymptotic ℓ p basis ( e i ). 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 0 if p = ∞).