Displaying similar documents to “A quasi-dichotomy for C(α,X) spaces, α < ω₁”

The basic sequence problem

N. Kalton (1995)

Studia Mathematica

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We construct a quasi-Banach space X which contains no basic sequence.

The controlled separable projection property for Banach spaces

Jesús Ferrer, Marek Wójtowicz (2011)

Open Mathematics

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Let X, Y be two Banach spaces. We say that Y is a quasi-quotient of X if there is a continuous operator R: X → Y such that its range, R(X), is dense in Y. Let X be a nonseparable Banach space, and let U, W be closed subspaces of X and Y, respectively. We prove that if X has the Controlled Separable Projection Property (CSPP) (this is a weaker notion than the WCG property) and Y is a quasi-quotient of X, then the structure of Y resembles the structure of a separable Banach space: (a)...

Uncomplemented copies of C(K) inside C(K).

Francisco Arranz (1996)

Extracta Mathematicae

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Throughout this note, whenever K is a compact space C(K) denotes the Banach space of continuous functions on K endowed with the sup norm. Though it is well known that every infinite dimensional Banach space contains uncomplemented subspaces, things may be different when only C(K) spaces are considered. For instance, every copy of l∞ = C(BN) is complemented wherever it is found. In [5] Pelzcynski found: Theorem 1. Let K be a compact metric space. If a separable Banach space X contains...

Uncountable sets of unit vectors that are separated by more than 1

Tomasz Kania, Tomasz Kochanek (2016)

Studia Mathematica

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Let X be a Banach space. We study the circumstances under which there exists an uncountable set 𝓐 ⊂ X of unit vectors such that ||x-y|| > 1 for any distinct x,y ∈ 𝓐. We prove that such a set exists if X is quasi-reflexive and non-separable; if X is additionally super-reflexive then one can have ||x-y|| ≥ slant 1 + ε for some ε > 0 that depends only on X. If K is a non-metrisable compact, Hausdorff space, then the unit sphere of X = C(K) also contains such a subset; if moreover...