Uniqueness of the topology on L¹(G)

J. Extremera; J. F. Mena; A. R. Villena

Displaying similar documents to “Uniqueness of the topology on L¹(G)”

Operators determining the complete norm topology of C(K)

A. Villena (1997)

Studia Mathematica

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For any uniformly closed subalgebra A of C(K) for a compact Hausdorff space K without isolated points and $x_{0} \in A$ , we show that every complete norm on A which makes continuous the multiplication by $x_{0}$ is equivalent to $∥ \cdot ∥_{\infty}$ provided that $x_{0}^{- 1} (λ)$ has no interior points whenever λ lies in ℂ. Actually, these assertions are equivalent if A = C(K).

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...

Simple construction of spaces without the Hahn-Banach extension property

Jerzy Kąkol (1992)

Commentationes Mathematicae Universitatis Carolinae

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An elementary construction for an abundance of vector topologies $ξ$ on a fixed infinite dimensional vector space $E$ such that $(E, ξ)$ has not the Hahn-Banach extension property but the topological dual ${(E, ξ)}^{'}$ separates points of $E$ from zero is given.

Binormality of Banach spaces

Petr Holický (1997)

Commentationes Mathematicae Universitatis Carolinae

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We study binormality, a separation property of spaces endowed with two topologies known in the real analysis as the Luzin-Menchoff property. The main object of our interest are Banach spaces with their norm and weak topologies. We show that every separable Banach space is binormal and the space $ℓ^{\infty}$ is not binormal.

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

J. Reinermann (1969)

Matematički Vesnik

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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.

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.