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

Date

2019-01-01

Author

Uyanik, Elif
Yurdakul, Murat Hayrettin

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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.

Subject Keywords

Bounded operators, Unbounded operators, l-Kothe spaces

URI

https://hdl.handle.net/11511/30037

Journal

TURKISH JOURNAL OF MATHEMATICS

DOI

https://doi.org/10.3906/mat-1905-90

Collections

Graduate School of Natural and Applied Sciences, Article

Citation Formats

E. Uyanik and M. H. Yurdakul, “A remark on a paper of P. B. Djakov and M. S. Ramanujan,” TURKISH JOURNAL OF MATHEMATICS, vol. 43, no. 5, pp. 2494–2498, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30037.