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Weaker forms of continuity and vector-valued Riemann integration

M. A. Sofi (2012)

Colloquium Mathematicae

It was proved by Kadets that a weak*-continuous function on [0,1] taking values in the dual of a Banach space X is Riemann-integrable precisely when X is finite-dimensional. In this note, we prove a Fréchet-space analogue of this result by showing that the Riemann integrability holds exactly when the underlying Fréchet space is Montel.

Weighted Fréchet spaces of holomorphic functions

Elke Wolf (2006)

Studia Mathematica

This article deals with weighted Fréchet spaces of holomorphic functions which are defined as countable intersections of weighted Banach spaces of type H . We characterize when these Fréchet spaces are Schwartz, Montel or reflexive. The quasinormability is also analyzed. In the latter case more restrictive assumptions are needed to obtain a full characterization.

Weighted (LB)-spaces of holomorphic functions and the dual density conditions.

Elke Wolf (2005)

RACSAM

Consideramos límites inductivos ponderados de espacios de funciones holomorfas que están definidos como la unión numerable de espacios ponderados de Banach de tipo H∞. Estudiamos el problema de la descripción proyectiva y analizamos cuando estos espacios tienen la condición de densidad dual de Bierstedt y Bonet.

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