Displaying similar documents to “Uncountable sets of unit vectors that are separated by more than 1”

A New Hereditarily l^2 Banach Space

Petsoulas, Giorgos (2009)

Serdica Mathematical Journal

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2000 Mathematics Subject Classification: 46B20, 46B26. We construct a non-reflexive, l^2 saturated Banach space such that every non-reflexive subspace has non-separable dual.

A quasi-dichotomy for C(α,X) spaces, α < ω₁

Elói Medina Galego, Maurício Zahn (2015)

Colloquium Mathematicae

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We prove the following quasi-dichotomy involving the Banach spaces C(α,X) of all X-valued continuous functions defined on the interval [0,α] of ordinals and endowed with the supremum norm. Suppose that X and Y are arbitrary Banach spaces of finite cotype. Then at least one of the following statements is true. (1) There exists a finite ordinal n such that either C(n,X) contains a copy of Y, or C(n,Y) contains a copy of X. (2) For any infinite...

(I)-envelopes of unit balls and James' characterization of reflexivity

Ondřej F. K. Kalenda (2007)

Studia Mathematica

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We study the (I)-envelopes of the unit balls of Banach spaces. We show, in particular, that any nonreflexive space can be renormed in such a way that the (I)-envelope of the unit ball is not the whole bidual unit ball. Further, we give a simpler proof of James' characterization of reflexivity in the nonseparable case. We also study the spaces in which the (I)-envelope of the unit ball adds nothing.

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)...