Displaying similar documents to “Non-separable tree-like Banach spaces and Rosenthal's ℓ₁-theorem”

The Tree Property at ω₂ and Bounded Forcing Axioms

Sy-David Friedman, Víctor Torres-Pérez (2015)

Bulletin of the Polish Academy of Sciences. Mathematics

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We prove that the Tree Property at ω₂ together with BPFA is equiconsistent with the existence of a weakly compact reflecting cardinal, and if BPFA is replaced by BPFA(ω₁) then it is equiconsistent with the existence of just a weakly compact cardinal. Similarly, we show that the Special Tree Property for ω₂ together with BPFA is equiconsistent with the existence of a reflecting Mahlo cardinal, and if BPFA is replaced by BPFA(ω₁) then it is equiconsistent with the existence of just a Mahlo...

A tree axiom.

Kurepa, Đuro (1985)

Publications de l'Institut Mathématique. Nouvelle Série

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Rudin's Dowker space in the extension with a Suslin tree

Teruyuki Yorioka (2008)

Fundamenta Mathematicae

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We introduce a generalization of a Dowker space constructed from a Suslin tree by Mary Ellen Rudin, and the rectangle refining property for forcing notions, which modifies the one for partitions due to Paul B. Larson and Stevo Todorčević and is stronger than the countable chain condition. It is proved that Martin's Axiom for forcing notions with the rectangle refining property implies that every generalized Rudin space constructed from Aronszajn trees is non-Dowker, and that the same...

A note on the structure of WUR Banach spaces

Spiros A. Argyros, Sophocles Mercourakis (2005)

Commentationes Mathematicae Universitatis Carolinae

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We present an example of a Banach space E admitting an equivalent weakly uniformly rotund norm and such that there is no Φ : E → c 0 ( Γ ) , for any set Γ , linear, one-to-one and bounded. This answers a problem posed by Fabian, Godefroy, Hájek and Zizler. The space E is actually the dual space Y * of a space Y which is a subspace of a WCG space.

Multiplicative functionals on algebras of differentiable functions.

Jesús A. Jaramillo (1990)

Extracta Mathematicae

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Let Ω be an open subset of a real Banach space E and, for 1 ≤ m ≤, let C(Ω) denote the algebra of all m-times continuously Fréchet differentiable real functions defined on Ω. We are concerned here with the question as to wether every nonzero algebra homomorphism φ: C(Ω) → R is given by evaluation at some point of Ω, i.e., if there exists some a ∈ Ω such that φ(f) = f(a) for each f ∈ C(Ω). This problem has been considered in [1,4,5] and [6]. In [6], a positive answer is given in the case...