Über einen graphensatz für lineare abbildungen mit metrisierbarem zielraum

Abstract

In [2] those locally convex spaces E, called GN-spaces, were investigated, for which every closed linear mapping from E to any normed space F is continuous. Here we study the smaller class of spaces E, called GM-spaces, which arise by admitting now for F all metrizable locally convex spaces. The GM-spaces have characterizations and permanence properties similar to those for GN-spaces. Main results are the barrelledness of every dense subspace of a GM-space, the finite dimension of the bounded subsets of separated GM-spaces, an embedding theorem., and the existence of separated GM-spaces which do not have the finest locally convex topology.