Full paper in PDF:
$% J. Bonet and S. Dierolf, Fréchet spaces of Moscatelli Type,
Rev. Mat. Univ. Complut. Madrid 2 (1989), supplementary, 77–92.%$
Fréchet Spaces of Moscatelli Type
Departamento de Matemática Aplicada E.T.S. Arquitectura Universidad Politécnica c. de Vera E-46071 Valencia — Spain | FB IV Mathematik Universität Trier Postfach 3825 D-5500 Trier — F.R. Germany |
A certain class of Fréchet spaces, called of Moscatelli type, is introduced
and studied. Using some shifting device these Fréchet spaces are defined as
projective limits of Banach spaces
, where
is a normal Banach
sequence space and the
’s are Banach spaces. The duality between Fréchet
and (LB)-spaces of Moscatelli type is established and the following properties
of Fréchet spaces are characterized in the present context: distinguishedness,
quasinormability, Heinrich’s density condition, existence of a continuous norm
in the space or the bidual, and the properties (DN) and (
) of Vogt.
1980 Mathematics Subject Classification (1985 revision): 46A6, 46A12.