Antiproximinal sets in the Banach space $c(X)$

S. Cobzaş

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

Kamil John (2000)

Commentationes Mathematicae Universitatis Carolinae

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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 $L (X, Y) \neq K (X, Y)$ 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 $λ$ . ...

Examples of k-iterated spreading models

Spiros A. Argyros, Pavlos Motakis (2013)

Studia Mathematica

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It is shown that for every k ∈ ℕ and every spreading sequence eₙₙ that generates a uniformly convex Banach space E, there exists a uniformly convex Banach space $X_{k + 1}$ admitting eₙₙ as a k+1-iterated spreading model, but not as a k-iterated one.

Remarks and examples concerning distance ellipsoids

Dirk Praetorius (2002)

Colloquium Mathematicae

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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.

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

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

Studia Mathematica

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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.

On copies of $c_{0}$ in the bounded linear operator space

Juan Carlos Ferrando, J. M. Amigó (2000)

Czechoslovak Mathematical Journal

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In this note we study some properties concerning certain copies of the classic Banach space $c_{0}$ in the Banach space $ℒ (X, Y)$ of all bounded linear operators between a normed space $X$ and a Banach space $Y$ equipped with the norm of the uniform convergence of operators.

Separated sequences in uniformly convex Banach spaces

J. M. A. M. van Neerven (2005)

Colloquium Mathematicae

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We give a characterization of uniformly convex Banach spaces in terms of a uniform version of the Kadec-Klee property. As an application we prove that if (xₙ) is a bounded sequence in a uniformly convex Banach space X which is ε-separated for some 0 < ε ≤ 2, then for all norm one vectors x ∈ X there exists a subsequence $(x_{n_{j}})$ of (xₙ) such that $i n f_{j \neq k} | | x - (x_{n_{j}} - x_{n_{k}}) | | \geq 1 + δ_{X} (2 / 3 ε)$ , where $δ_{X}$ is the modulus of convexity of X. From this we deduce that the unit sphere of every infinite-dimensional uniformly convex Banach space...

Displaying similar documents to “Antiproximinal sets in the Banach space <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <mrow> <mi>c</mi> <mo>(</mo> <mi>X</mi> <mo>)</mo> </mrow> </math>”

Examples of k-iterated spreading models

Remarks and examples concerning distance ellipsoids

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

On copies of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"> <msub> <mi>c</mi> <mn>0</mn> </msub> </math> in the bounded linear operator space

Separated sequences in uniformly convex Banach spaces

Displaying similar documents to “Antiproximinal sets in the Banach space $c (X)$ ”

On copies of $c_{0}$ in the bounded linear operator space