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Factorization of unbounded operators on Köthe spaces

Terzioğlu, Tosun and Yurdakul, Emin and Zakharyuta, Vyacheslav (2004) Factorization of unbounded operators on Köthe spaces. Studia Mathematica, 161 (1). pp. 61-70. ISSN 0039-3223 (Print) 1730-6337 (Online)

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Official URL: http://dx.doi.org/10.4064/sm161-1-4

Abstract

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]).

Item Type:Article
Uncontrolled Keywords:locally convex spaces; unbounded operators; Kothe spaces; bounded factorization property
Subjects:Q Science > QA Mathematics
ID Code:425
Deposited By:Vyacheslav Zakharyuta
Deposited On:14 Oct 2005 03:00
Last Modified:24 Jun 2013 15:30

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