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1

An almost nowhere Fréchet smooth norm on superreflexive spaces

100%

Matoušková E.

Studia Mathematica

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1999

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tom 133

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nr 1

93-99

EN

Every separable infinite-dimensional superreflexive Banach space admits an equivalent norm which is Fréchet differentiable only on an Aronszajn null set.

2

A note on intersections of non-Haar null sets

63%

Matoušková E., Zelený M.

Colloquium Mathematicum

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2003

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tom 96

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nr 1

1-4

EN

We show that in every Polish, abelian, non-locally compact group G there exist non-Haar null sets A and B such that the set {g ∈ G; (g+A) ∩ B is non-Haar null} is empty. This answers a question posed by Christensen.

3

Reflexivity and approximate fixed points

63%

Matoušková E., Reich S.

Studia Mathematica

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2003

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tom 159

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nr 3

403-415

EN

A Banach space X is reflexive if and only if every bounded sequence {xₙ} in X contains a norm attaining subsequence. This means that it contains a subsequence ${x_{n_k}}$ for which $sup_{f∈S_{X*}} lim sup_{k→∞} f(x_{n_k})$ is attained at some f in the dual unit sphere $S_{X*}$. A Banach space X is not reflexive if and only if it contains a normalized sequence {xₙ} with the property that for every $f ∈ S_{X*}$, there exists $g ∈ S_{X*}$ such that $lim sup_{n→∞}f(xₙ) < lim inf_{n→∞}g(xₙ)$. Combining this with a result of Shafrir, we conclude that every infinite-dimensional Banach space contains an unbounded closed convex set which has the approximate fixed point property for nonexpansive mappings.

Ograniczanie wyników

2 Studia Mathematica

1 Colloquium Mathematicum

3 Matoušková E.

1 Reich S.

1 Zelený M.

2 2003

1 1999

An almost nowhere Fréchet smooth norm on superreflexive spaces

A note on intersections of non-Haar null sets

Reflexivity and approximate fixed points