Reflexivity and the separable quotient problem for a class of Banach spaces

• Autorzy: Wójtowicz M.
• Języki publikacji: EN

Abstrakty

EN

Let E be a Banach lattice and let X be its closed subspace such that: X is complemented in E, or the norm of E is order continuous. Then X is reflexive iff X* contains no isomorphic copy of l₁ iff for every n ≥ l, the nth dual X⁽ⁿ⁾ of X contains no isomorphic copy of l₁ iff X has no quotient isomorphic to c₀ and X does not have a subspace isomorphic to l₁ (Theorem 2). This is an extension of the results obtained earlier by Lozanovskiĭ, Tzafriri, Meyer-Nieberg, and Diaz and Fernández. The theorem is applied to show that many Banach spaces possess separable quotients isomorphic to one of the following spaces: c₀, l₁, or a reflexive space with a Schauder basis.

Słowa kluczowe

EN

Banach lattices; embeddability of l1; reflexivity of Banach spaces; separable quotients of Banach spaces

PL

krata Banacha; refleksywna przestrzeń Banacha; refleksywność w przestrzeniach Banacha; włożoność z l1

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2002
• Tom: Vol. 50, no 4
• Strony: 383--394
• Opis fizyczny: Bibliogr. 36 poz.

Twórcy

autor

Wójtowicz M.

• Institute of Mathematics, University of Zielona Góra, Podgórna 50, 65-246 Zielona Góra, Poland

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