Full paper in PDF:
$% K. D. Bierstedt and J. Bonet, Density conditions in Fréchet and (DF)-spaces,
Rev. Mat. Univ. Complut. Madrid 2 (1989), supplementary, 59–75.%$
Density Conditions in Fréchet and (DF)-Spaces
|
FB 17, Mathemathik Universität-GH-Paderborn Postfach 16 21 D-4790 Paderborn Federal Republic of Germany |
Departamento de Matemáticas E.T.S. Arquitectura Universidad Politécnica de Valencia Camino de Vera E-46071 Valencia — Spain |
We survey our main results on the density condition for Fréchet spaces and on the dual density condition for (DF)-spaces (cf. Bierstedt and Bonet (1988)) as well as some recent developments.
At the end of section 1, we include a new result on the projective tensor
product of two Fréchet spaces. Taskinen’s construction of counterexamples to
Grothendieck’s “problème des topologies” yields Fréchet spaces
,
with the
density condition such that
is not (even) distinguished (see Taskinen
(to appear)). We prove now that the negative solution of the “problème des
topologies” is, in fact, the only obstruction: For two Fréchet spaces
and
with the density condition,
has the density condition as well (and hence
is distinguished) whenever the “problème des topologies” has a positive solution
for the pair
.
1980 Mathematics Subject Classification (1985 revision): 46A06, 46A07, 46A09, 46A020, 46A32, 46A45, 46M05, 46M40.