A remark on a paper of P. B. Djakov and M. S. Ramanujan

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UYANIK E., YURDAKUL M. H.

TURKISH JOURNAL OF MATHEMATICS, cilt.43, sa.5, ss.2494-2498, 2019 (SCI-Expanded, Scopus, TRDizin)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 43 Sayı: 5
• Basım Tarihi: 2019
• Doi Numarası: 10.3906/mat-1905-90
• Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
• Sayfa Sayıları: ss.2494-2498
• Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
• Yozgat Bozok Üniversitesi Adresli: Evet

Özet

Let l be a Banach sequence space with a monotone norm in which the canonical system (e(n)) is an unconditional basis. We show that if there exists a continuous linear unbounded operator between l-Kothe spaces, then there exists a continuous unbounded quasidiagonal operator between them. Using this result, we study the corresponding Kothe matrices when every continuous linear operator between l-Kothe spaces is bounded. As an application, we observe that the existence of an unbounded operator between l-Kothe spaces, under a splitting condition, causes the existence of a common basic subspace.