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2004 | 161 | 1 | 61-70
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Factorization of unbounded operators on Köthe spaces

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The main result is that the existence of an unbounded continuous linear operator T between Köthe spaces λ(A) and λ(C) which factors through a third Köthe space λ(B) causes the existence of an unbounded continuous quasidiagonal operator from λ(A) into λ(C) factoring through λ(B) as a product of two continuous quasidiagonal operators. This fact is a factorized analogue of the Dragilev theorem [3, 6, 7, 2] about the quasidiagonal characterization of the relation (λ(A),λ(B)) ∈ ℬ (which means that all continuous linear operators from λ(A) to λ(B) are bounded). The proof is based on the results of [9] where the bounded factorization property ℬ F is characterized in the spirit of Vogt's [10] characterization of ℬ. As an application, it is shown that the existence of an unbounded factorized operator for a triple of Köthe spaces, under some additonal asumptions, causes the existence of a common basic subspace at least for two of the spaces (this is a factorized analogue of the results for pairs [8, 2]).
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Twórcy
  • Sabancı University, 81474 Tuzla-Istanbul, Turkey
autor
  • Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey
autor
  • Department of Mathematics, Middle East Technical University, & Faculty of Engineering and Natural Sciences, Sabancı University, 81474 Tuzla-Istanbul, Turkey
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_4064-sm161-1-4
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