Factorization of unbounded operators on Köthe spaces

• Autorzy: T. Terzioğlu , M. Yurdakul , V. Zahariuta
• Języki publikacji: EN

Abstrakty

EN

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]).

Kategorie tematyczne

• 46A20: Duality theory
• 46A04: Locally convex Fr\'echet spaces and (DF)-spaces
• 46A32: Spaces of linear operators; topological tensor products; approximation properties
• 46A13: Spaces defined by inductive or projective limits (LB, LF, etc.)
• 46A03: General theory of locally convex spaces
• 47L05: Linear spaces of operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 161
• Numer: 1
• Strony: 61-70

Daty

wydano

2004

Twórcy

autor

T. Terzioğlu

• Sabancı University, 81474 Tuzla-Istanbul, Turkey

autor

M. Yurdakul

• Department of Mathematics, Middle East Technical University, 06531 Ankara, Turkey

autor

V. Zahariuta

• Department of Mathematics, Middle East Technical University, & Faculty of Engineering and Natural Sciences, Sabancı University, 81474 Tuzla-Istanbul, Turkey

Identyfikatory

DOI

10.4064/sm161-1-4