Turkish Journal of Mathematics
Abstract
Let $\ell$ 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 $\ell$-Köthe spaces, then there exists a continuous unbounded quasidiagonal operator between them. Using this result, we study the corresponding Köthe matrices when every continuous linear operator between $\ell$-Köthe spaces is bounded. As an application, we observe that the existence of an unbounded operator between $\ell$-Köthe spaces, under a splitting condition, causes the existence of a common basic subspace.
DOI
10.3906/mat-1905-90
Keywords
Bounded operators, unbounded operators, $\ell$-Köthe spaces
First Page
2494
Last Page
2498
Recommended Citation
UYANIK, E, & YURDAKUL, M. H (2019). A remark on a paper of P. B. Djakov and M. S. Ramanujan. Turkish Journal of Mathematics 43 (5): 2494-2498. https://doi.org/10.3906/mat-1905-90
