On strongly asymptotic  l   p   spaces and minimality | Zendy

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

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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 = ∞).

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