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Displaying similar documents to “Characterizations of L 1 -predual spaces by centerable subsets”

Banach spaces which admit a norm with the uniform Kadec-Klee property

S. Dilworth, Maria Girardi, Denka Kutzarova (1995)

Studia Mathematica

Similarity:

Several results are established about Banach spaces Ӿ which can be renormed to have the uniform Kadec-Klee property. It is proved that all such spaces have the complete continuity property. We show that the renorming property can be lifted from Ӿ to the Lebesgue-Bochner space L 2 ( Ӿ ) if and only if Ӿ is super-reflexive. A basis characterization of the renorming property for dual Banach spaces is given.

Antiproximinal sets in the Banach space c ( X )

S. Cobzaş (1997)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

If X is a Banach space then the Banach space c ( X ) of all X -valued convergent sequences contains a nonvoid bounded closed convex body V such that no point in C ( X ) V has a nearest point in V .

Remarks and examples concerning distance ellipsoids

Dirk Praetorius (2002)

Colloquium Mathematicae

Similarity:

We provide for every 2 ≤ k ≤ n an n-dimensional Banach space E with a unique distance ellipsoid such that there are precisely k linearly independent contact points between and B E . The corresponding result holds for spaces with non-unique distance ellipsoids as well. We construct n-dimensional Banach spaces E such that one distance ellipsoid has precisely k linearly independent contact points and all other distance ellipsoids have less than k-1 such points.

Multiplying balls in the space of continuous functions on [0,1]

Marek Balcerzak, Artur Wachowicz, Władysław Wilczyński (2005)

Studia Mathematica

Similarity:

Let C denote the Banach space of real-valued continuous functions on [0,1]. Let Φ: C × C → C. If Φ ∈ +, min, max then Φ is an open mapping but the multiplication Φ = · is not open. For an open ball B(f,r) in C let B²(f,r) = B(f,r)·B(f,r). Then f² ∈ Int B²(f,r) for all r > 0 if and only if either f ≥ 0 on [0,1] or f ≤ 0 on [0,1]. Another result states that Int(B₁·B₂) ≠ ∅ for any two balls B₁ and B₂ in C. We also prove that if Φ ∈ +,·,min,max, then the set Φ - 1 ( E ) is residual whenever E is...

The Dual of a Non-reflexive L-embedded Banach Space Contains l Isometrically

Hermann Pfitzner (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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A Banach space is said to be L-embedded if it is complemented in its bidual in such a way that the norm between the two complementary subspaces is additive. We prove that the dual of a non-reflexive L-embedded Banach space contains l isometrically.

Projections from L ( X , Y ) onto K ( X , Y )

Kamil John (2000)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Generalization of certain results in [Sap] and simplification of the proofs are given. We observe e.g.: Let X and Y be Banach spaces such that X is weakly compactly generated Asplund space and X * has the approximation property (respectively Y is weakly compactly generated Asplund space and Y * has the approximation property). Suppose that L ( X , Y ) K ( X , Y ) and let 1 < λ < 2 . Then X (respectively Y ) can be equivalently renormed so that any projection P of L ( X , Y ) onto K ( X , Y ) has the sup-norm greater or equal to λ . ...

The structure of Lindenstrauss-Pełczyński spaces

Jesús M. F. Castillo, Yolanda Moreno, Jesús Suárez (2009)

Studia Mathematica

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Lindenstrauss-Pełczyński (for short ℒ) spaces were introduced by these authors [Studia Math. 174 (2006)] as those Banach spaces X such that every operator from a subspace of c₀ into X can be extended to the whole c₀. Here we obtain the following structure theorem: a separable Banach space X is an ℒ-space if and only if every subspace of c₀ is placed in X in a unique position, up to automorphisms of X. This, in combination with a result of Kalton [New York J. Math. 13 (2007)], provides...

An indecomposable Banach space of continuous functions which has small density

Rogério Augusto dos Santos Fajardo (2009)

Fundamenta Mathematicae

Similarity:

Using the method of forcing we construct a model for ZFC where CH does not hold and where there exists a connected compact topological space K of weight ω < 2 ω such that every operator on the Banach space of continuous functions on K is multiplication by a continuous function plus a weakly compact operator. In particular, the Banach space of continuous functions on K is indecomposable.