On a fixed-point theorem of Banach-type for uniform spaces

J. Reinermann

Displaying similar documents to “On a fixed-point theorem of Banach-type for uniform spaces”

The compact weak topology on a Banach space.

Manuel González, Joaquín M. Gutiérrez (1990)

Extracta Mathematicae

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Throughout [this paper], E and F will denote Banach spaces. The bounded weak topology on a Banach space E, noted bw(E) or simply bw, is defined as the finest topology that agrees with the weak topology on bounded sets. It is proved in [3] that bw(E) is a locally convex topology if and only if E is reflexive. In this paper we introduce the compact weak topology on a Banach space E, noted kw(E) or simply kw, as the finest topology that agrees with the weak topology on weakly...

Banach Spaces Determined by Their Uniform Structures.

W.B. Johnson, J. Lindenstrauss (1996)

Geometric and functional analysis

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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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Regulated functions

Dana Fraňková (1991)

Mathematica Bohemica

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The first section consists of auxiliary results about nondecreasing real functions. In the second section a new characterization of relatively compact sets of regulated functions in the sup-norm topology is brought, and the third section includes, among others, an analogue of Helly's Choice Theorem in the space of regulated functions.

C(K) spaces which cannot be uniformly embedded into c₀(Γ)

Jan Pelant, Petr Holický, Ondřej F. K. Kalenda (2006)

Fundamenta Mathematicae

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We give two examples of scattered compact spaces K such that C(K) is not uniformly homeomorphic to any subset of c₀(Γ) for any set Γ. The first one is [0,ω₁] and hence it has the smallest possible cardinality, the other one has the smallest possible height ω₀ + 1.

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.

Uniform homeomorphisms between Banach spaces

P. Enflo (1975-1976)

Séminaire Analyse fonctionnelle (dit "Maurey-Schwartz")

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Uniqueness of the topology on L¹(G)

J. Extremera, J. F. Mena, A. R. Villena (2002)

Studia Mathematica

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Let G be a locally compact abelian group and let X be a translation invariant linear subspace of L¹(G). If G is noncompact, then there is at most one Banach space topology on X that makes translations on X continuous. In fact, the Banach space topology on X is determined just by a single nontrivial translation in the case where the dual group Ĝ is connected. For G compact we show that the problem of determining a Banach space topology on X by considering translation operators on X is...

On a certain class of $Λ$ -structures. I

Stanislav Tomášek (1970)

Czechoslovak Mathematical Journal

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Uniform Eberlein Compacta and Uniformly Gâteaux Smooth Norms

Fabian, Marián, Hájek, Petr, Zizler, Václav (1997)

Serdica Mathematical Journal

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* Supported by grants: AV ĈR 101-95-02, GAĈR 201-94-0069 (Czech Republic) and NSERC 7926 (Canada). It is shown that the dual unit ball BX∗ of a Banach space X∗ in its weak star topology is a uniform Eberlein compact if and only if X admits a uniformly Gâteaux smooth norm and X is a subspace of a weakly compactly generated space. The bidual unit ball BX∗∗ of a Banach space X∗∗ in its weak star topology is a uniform Eberlein compact if and only if X admits a weakly uniformly...