Some Remarks on the Weak Topology of Locally Convex Spaces

Stojan Radenović

Displaying similar documents to “Some Remarks on the Weak Topology of Locally Convex 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...

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.