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Fréchet spaces of Moscatelli type. (English) Zbl 0757.46001

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.

MSC:

46A04 Locally convex Fréchet spaces and (DF)-spaces
46A13 Spaces defined by inductive or projective limits (LB, LF, etc.)
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