Uniform Kadec-Klee property and nearly uniform convexity in Köthe-Bochner sequence spaces

Paweł Kolwicz

Displaying similar documents to “Uniform Kadec-Klee property and nearly uniform convexity in Köthe-Bochner sequence spaces”

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.

A nearly uniformly convex space which is not a $(β)$ -space

Denka Kutzarova (1989)

Acta Universitatis Carolinae. Mathematica et Physica

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On two classes of Banach spaces with uniform normal structure

Ji Gao, Ka-Sing Lau (1991)

Studia Mathematica

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Geometry of quotient spaces and proximinality

Yuan Cui, Henryk Hudzik, Yaowaluck Khongtham (2003)

Annales Polonici Mathematici

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It is proved that if X is a rotund Banach space and M is a closed and proximinal subspace of X, then the quotient space X/M is also rotund. It is also shown that if Φ does not satisfy the δ₂-condition, then $h ⁰_{Φ}$ is not proximinal in $l ⁰_{Φ}$ and the quotient space $l ⁰_{Φ} / h ⁰_{Φ}$ is not rotund (even if $l ⁰_{Φ}$ is rotund). Weakly nearly uniform convexity and weakly uniform Kadec-Klee property are introduced and it is proved that a Banach space X is weakly nearly uniformly convex if and only if it is reflexive and...

Separated sequences in asymptotically uniformly convex Banach spaces

Sylvain Delpech (2010)

Colloquium Mathematicae

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We prove that the unit sphere of every infinite-dimensional Banach space X contains an α-separated sequence, for every $0 < α < 1 + δ ̅_{X} (1)$ , where $δ ̅_{X}$ denotes the modulus of asymptotic uniform convexity of X.

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.

Estimates for Kottman's separation constant in reflexive Banach spaces

Elisabetta Maluta, Pier Luigi Papini (2009)

Colloquium Mathematicae

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In reflexive Banach spaces with some degree of uniform convexity, we obtain estimates for Kottman's separation constant in terms of the corresponding modulus.

$w^{*}$ -basic sequences and reflexivity of Banach spaces

Kamil John (2005)

Czechoslovak Mathematical Journal

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We observe that a separable Banach space $X$ is reflexive iff each of its quotients with Schauder basis is reflexive. Similarly if $ℒ (X, Y)$ is not reflexive for reflexive $X$ and $Y$ then $ℒ (X_{1}, Y)$ is is not reflexive for some $X_{1} \subset X$ , $X_{1}$ having a basis.

Noncommutative uniform algebras

Mati Abel, Krzysztof Jarosz (2004)

Studia Mathematica

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We show that a real Banach algebra A such that ||a²|| = ||a||² for a ∈ A is a subalgebra of the algebra $C_{ℍ} (X)$ of continuous quaternion-valued functions on a compact set X.