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

José BONET and Suzanne DIEROLF
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

ABSTRACT

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 L((Xk)k (- N)  , where L  is a normal Banach sequence space and the Xk  ’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 (_O_  ) of Vogt.

1980 Mathematics Subject Classification (1985 revision): 46A6, 46A12.