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A conjecture of Palamodov about the functors Ext k in the category of locally convex spaces
Ist Teil von
Journal of functional analysis, 2003, Vol.201 (2), p.561-571
Ort / Verlag
Elsevier Inc
Erscheinungsjahr
2003
Link zum Volltext
Quelle
EZB Electronic Journals Library
Beschreibungen/Notizen
In 1971 Palamodov proved that in the category of locally convex spaces the derived functors Ext
k
(
E,
X) of Hom(
E,·) all vanish if
E is a (DF)-space,
X is a Fréchet space, and one of them is nuclear. He conjectured a “dual result”, namely that Ext
k
(
E,
X)=0 for all
k∈
N
if
E is a metrizable locally convex space,
X is a complete (DF)-space, and one of them is nuclear. Assuming the continuum hypothesis we give a complete answer to this conjecture: If
X is an infinite-dimensional nuclear (DF)-space, then
(1)
There is a normed space
E such that Ext
1(
E,
X)≠0.
(2)
Ext
2(
K
N
,X)≠0
where
K
N
is a countable product of lines.
(3)
Ext
k
(
E,
X)=0 for all
k⩾3 and all locally convex spaces
E.