Factorization of unbounded operators on Köthe spaces

T. Terzioğlu, M. Yurdakul, and V. Zahariuta. "Factorization of unbounded operators on Köthe spaces." Studia Mathematica 161.1 (2004): 61-70. <http://eudml.org/doc/285189>.

@article{T2004,
abstract = {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]).},
author = {T. Terzioğlu, M. Yurdakul, V. Zahariuta},
journal = {Studia Mathematica},
keywords = {quasidiagonal operators; locally convex spaces; bounded factorization property},
language = {eng},
number = {1},
pages = {61-70},
title = {Factorization of unbounded operators on Köthe spaces},
url = {http://eudml.org/doc/285189},
volume = {161},
year = {2004},
}

TY - JOUR
AU - T. Terzioğlu
AU - M. Yurdakul
AU - V. Zahariuta
TI - Factorization of unbounded operators on Köthe spaces
JO - Studia Mathematica
PY - 2004
VL - 161
IS - 1
SP - 61
EP - 70
AB - 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]).
LA - eng
KW - quasidiagonal operators; locally convex spaces; bounded factorization property
UR - http://eudml.org/doc/285189
ER -