Bonet, José; Dierolf, Susanne Fréchet spaces of Moscatelli type. (English) Zbl 0757.46001 Rev. Mat. Univ. Complutense Madr. 2, Suppl., 77-92 (1989). Summary: 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 \(L((X_ k)_{k\in\mathbb{N}})\), where \(L\) is a normal Banach sequence space and the \(X_ k\)’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 \((\Omega)\) of Vogt. Cited in 2 ReviewsCited in 13 Documents MSC: 46A04 Locally convex Fréchet spaces and (DF)-spaces 46A13 Spaces defined by inductive or projective limits (LB, LF, etc.) Keywords:Fréchet spaces; projective limits of Banach spaces; duality between Fréchet and \((LB)\)-spaces of Moscatelli type; distinguishedness; quasinormability; Heinrich’s density condition; existence of a continuous norm; properties \((DN)\) and \((\Omega)\) of Vogt PDFBibTeX XMLCite \textit{J. Bonet} and \textit{S. Dierolf}, Rev. Mat. Univ. Complutense Madr. 2, 77--92 (1989; Zbl 0757.46001) Full Text: EuDML