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On Mackey topology for groups

M. Chasco; E. Martín-Peinador; V. Tarieladze — 1999

Studia Mathematica

The present paper is a contribution to fill in a gap existing between the theory of topological vector spaces and that of topological abelian groups. Topological vector spaces have been extensively studied as part of Functional Analysis. It is natural to expect that some important and elegant theorems about topological vector spaces may have analogous versions for abelian topological groups. The main obstruction to get such versions is probably the lack of the notion of convexity in the framework...

Two geometric constants for operators acting on a separable Banach space.

E. Martín Peinador; E. Induráin; A. Plans Sanz de Bremond; A. A. Rodes Usan — 1988

Revista Matemática de la Universidad Complutense de Madrid

The main result of this paper is the following: A separable Banach space X is reflexive if and only if the infimum of the Gelfand numbers of any bounded linear operator defined on X can be computed by means of just one sequence on nested, closed, finite codimensional subspaces with null intersection.

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