1985
DOI: 10.1007/bf01215139
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The splitting relation for K�the spaces

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Cited by 21 publications
(13 citation statements)
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“…They showed, in particular, that if the spaces satisfy a splitting condition of Apiola type [1], then the existence of an unbounded operator implies the existence of a common basic subspace. Djakov and Ramanujan [2] obtain the same result without the assumption of nuclearity and assuming the weaker splitting condition of Krone and Vogt [5].…”
Section: Proposition 2 We Have (λ(A) λ(B) λ(C)) ∈ Bf If and Only Imentioning
confidence: 53%
See 1 more Smart Citation
“…They showed, in particular, that if the spaces satisfy a splitting condition of Apiola type [1], then the existence of an unbounded operator implies the existence of a common basic subspace. Djakov and Ramanujan [2] obtain the same result without the assumption of nuclearity and assuming the weaker splitting condition of Krone and Vogt [5].…”
Section: Proposition 2 We Have (λ(A) λ(B) λ(C)) ∈ Bf If and Only Imentioning
confidence: 53%
“…This is a generalization of Proposition 3.4 from [5], where the case of Köthe spaces was considered (for Köthe spaces the conditions S and S coincide): basically, our proof of Proposition 7 is a generalized direct version of the proof ad absurdum from [5] Proof. Because of complete similarity we consider only the case S. Suppose that (F, E) ∈ S. Then there is a function τ : N → N such that for each T ∈ L(E, F ) the estimate…”
Section: Now We Consider a Factorized Analogue Of The Condition S A mentioning
confidence: 85%
“…As the topological duals of k 0 (A) ⊗ ε F and k 0 (A) ⊗ π F coincide, we have to show that ε also equals τ . From L(F, λ 1 (A)) = LB(F, λ 1 (A)) we deduce that the pair (λ 1 (A), F ) fulfills condition (S * 2 ) (see [19,Proposition 3.4]). If λ 1 (A) is countably normed this implies the condition (S 2 ) (see proof of Theorem 2.1).…”
Section: Wwwmn-journalcommentioning
confidence: 99%
“…Using the well-known condition (S * 2 ) of D. Vogt, which plays a central role in the theory of splitting sequences of Fréchet spaces (see [12] and [29]), J. Krone and D. Vogt characterized the barrelledness of the space L b λ 1 (A), λ 1 (B) under the assumption of λ 1 (A) being Schwartz ( [19,Theorem 2.1]). This was generalized by E. Mangino for distinguished λ 1 (A) and an arbitrary Fréchet space instead of λ 1 (B) ([23, Corollary 1]) using fundamental results concerning proj 1 X = 0 (see [8] and [12]).…”
Section: Introductionmentioning
confidence: 99%
“…If Q is the principal part of P, then P = Q + R with R := P -Q. For [20] together with the representation of ker P ( D ) as a tensor product shows that ker P(D) is not bornological (b) M. LANGENBRUCH has pointed out that Lemma 5.1 can be improved if one uses a sequence space representation for ker P(D) which follows from LANGENBRUCH [21] to show that ker P ( D ) is not bornological.…”
Section: Examplesmentioning
confidence: 99%