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]).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm161-1-4,
author = {T. Terzio\u glu and M. Yurdakul and V. Zahariuta},
title = {Factorization of unbounded operators on K\"othe spaces},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {61-70},
zbl = {1062.46008},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm161-1-4}
}
T. Terzioğlu; M. Yurdakul; V. Zahariuta. Factorization of unbounded operators on Köthe spaces. Studia Mathematica, Tome 162 (2004) pp. 61-70. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm161-1-4/