The existence of a factorized unbounded operator between Fréchet spaces
2018 ◽
Vol 13
(01)
◽
pp. 2050017
Keyword(s):
For locally convex spaces [Formula: see text] and [Formula: see text], the continuous linear map [Formula: see text] is called bounded if there is a zero neighborhood [Formula: see text] of [Formula: see text] such that [Formula: see text] is bounded in [Formula: see text]. Our main result is that the existence of an unbounded operator [Formula: see text] between Fréchet spaces [Formula: see text] and [Formula: see text] which factors through a third Fréchet space [Formula: see text] ends up with the fact that the triple [Formula: see text] has an infinite dimensional closed common nuclear Köthe subspace, provided that [Formula: see text] has the property [Formula: see text].
1974 ◽
Vol 26
(6)
◽
pp. 1294-1300
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Keyword(s):
1990 ◽
Vol 13
(3)
◽
pp. 607-610
Keyword(s):
2003 ◽
Vol 13
(07)
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pp. 1649-1655
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Keyword(s):
1975 ◽
Vol 27
(5)
◽
pp. 1110-1113
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1975 ◽
Vol 79
◽
pp. 441-509
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1982 ◽
Vol 108
(1)
◽
pp. 275-297
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1999 ◽
Vol 02
(03)
◽
pp. 427-440
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Keyword(s):
Keyword(s):