Boundaries, Martin's Axiom, and (P)-properties in dual Banach spaces

• Autorzy: Granero A. S. , Hernández J. M.

Identyfikatory

DOI

10.14708/cm.v56i1.1108

• Języki publikacji: EN

Abstrakty

EN

Let X be a~Banach space and Seq(X^∗∗) (resp., Xℵ0) the subset of elements ψ∈X^∗∗ such that there exists a~sequence (xn)n≥1⊂X such that xn→ψ in the ω^∗-topology of X^∗∗ (resp., there exists a~separable subspace Y⊂X such that ψ∈Y¯¯¯¯ω^∗). Then: (i) if Dens(X)≥ℵ1, the property X^∗∗=Xℵ0 (resp., X^∗∗=Seq(X^∗∗)) is ℵ1-determined, i.e., X~has this property iff Y has, for every subspace Y⊂X with Dens(Y)=ℵ1; (ii) if X^∗∗=X_ℵ0, (B(X^∗∗),ω^∗) has countable tightness; (iii) under the Martin's axiom MA(ω₁) we have X^∗∗=Seq(X>∗∗) iff (B(X^∗),ω^∗) has countable tightness and overlineco(B)=co¯¯¯¯¯ω^∗(K) for every subspace Y⊂X, every ω^∗-compact subset K of Y^∗, and every boundary B⊂K .

Słowa kluczowe

EN

boundaries; Martin's Axiom; equality Seq(X∗∗)=X∗∗; super-(P) property

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2016
• Tom: Vol 56, No. 1
• Strony: 1--16
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Granero A. S.

• Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense, 28040-Madrid, Spain

autor

Hernández J. M.

• Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense, 28040-Madrid, Spain

Bibliografia

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Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.