This article presents results about the class of locally convex spaces which are defined as the intersection $E\cap F$ of a Fréchet space $F$ and a countable inductive limit of Banach spaces $E$. This class appears naturally in analytic applications to linear partial differential operators. The intersection has two natural topologies, the intersection topology an an inductive topology. The first one is easier to describe and the second one has good locally convex properties. The coincidence of these topolgies and its consequences for the spaces $E\cap F$ and $E+F$ are investigated.
Intersections of Fréchet spaces and (LB)-spaces
ALBANESE, Angela Anna;
2006-01-01
Abstract
This article presents results about the class of locally convex spaces which are defined as the intersection $E\cap F$ of a Fréchet space $F$ and a countable inductive limit of Banach spaces $E$. This class appears naturally in analytic applications to linear partial differential operators. The intersection has two natural topologies, the intersection topology an an inductive topology. The first one is easier to describe and the second one has good locally convex properties. The coincidence of these topolgies and its consequences for the spaces $E\cap F$ and $E+F$ are investigated.File in questo prodotto:
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