1990
DOI: 10.1007/bf01188687
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Unbounded linear operators and nuclear Köthe quotients

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Cited by 14 publications
(9 citation statements)
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“…Recall that a Fréchet space is not a prequojection if and only if it admits a separated quotient isomorphic to an infinite dimensional nuclear Köthe echelon space, see [5,14,33,37]. This fact, together with Propositions 3.2 and 3.4, suggest the following Question 1.…”
Section: Proposition 34 Let X Be a Prequojection Fréchet Space Thementioning
confidence: 90%
See 1 more Smart Citation
“…Recall that a Fréchet space is not a prequojection if and only if it admits a separated quotient isomorphic to an infinite dimensional nuclear Köthe echelon space, see [5,14,33,37]. This fact, together with Propositions 3.2 and 3.4, suggest the following Question 1.…”
Section: Proposition 34 Let X Be a Prequojection Fréchet Space Thementioning
confidence: 90%
“…It is known that X is a prequojection if and only if X β is a strict (LB)-space. An alternative characterization is that X is a prequojection if and only if X has no nuclear quotient which admits a continuous norm, see [5,14,33,37]. The problem of the existence of non-trivial prequojections arose in a natural way in [5]; it has been solved, in the positive sense, in various papers, [6,14,32].…”
Section: Proposition 32mentioning
confidence: 98%
“…The following two notions, introduced in [22,23,30], are defined here in a slightly different equivalent form.…”
Section: (P)mentioning
confidence: 99%
“…Quojections are important tools in Fréchet spaces theory. Recall that, by the results of S. F. Bellenot and E. Dubinsky [1], D. Vogt [24], and S.Önal and T. Terzioǧlu [10], a Fréchet space E has a nuclear Köthe quotient if and only if the strong bidual of E is not quojection (compare with Theorem 3.4).…”
Section: Introductionmentioning
confidence: 98%