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A remark on a paper of P. B. Djakov and M. S. Ramanujan
Date
2019-01-01
Author
Uyanik, Elif
Yurdakul, Murat Hayrettin
Metadata
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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
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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.