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

2019-01-01
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.
TURKISH JOURNAL OF MATHEMATICS

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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, pp. 2494–2498, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/30037.