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Factorization of unbounded operators on Kothe spaces
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Date
2004-01-01
Author
Terzioglou, T
Yurdakul, Murat Hayrettin
Zuhariuta, V
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The main result is that the existence of an unbounded continuous linear operator T between Kothe spaces lambda(A) and lambda(C) which factors through a third Kothe space A(B) causes the existence of an unbounded continuous quasidiagonal operator from lambda(A) into lambda(C) factoring through lambda(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 (lambda(A), lambda(B)) is an element of B (which means that all continuous linear operators from lambda(A) to lambda(B) are bounded). The proof is based on the results of [9) where the bounded factorization property BF 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 Kothe 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]).
Subject Keywords
Locally convex spaces
,
Unbounded operators
,
Köthe spaces
,
Bounded factorization property
URI
https://hdl.handle.net/11511/31969
Journal
STUDIA MATHEMATICA
DOI
https://doi.org/10.4064/sm161-1-4
Collections
Graduate School of Natural and Applied Sciences, Article
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T. Terzioglou, M. H. Yurdakul, and V. Zuhariuta, “Factorization of unbounded operators on Kothe spaces,”
STUDIA MATHEMATICA
, pp. 61–70, 2004, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/31969.