Factorization of unbounded operators on Kothe spaces
STUDIA MATHEMATICA, cilt.161, sa.1, ss.61-70, 2004 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 161 Sayı: 1
- Basım Tarihi: 2004
- Doi Numarası: 10.4064/sm161-1-4
- Dergi Adı: STUDIA MATHEMATICA
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.61-70
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
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]).