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

Authors : Elif Uyanik, Murat Hayrettin Yurdakul

Pages : 2494-2498

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Publication Date : 9999-12-31

Article Type : Makaleler

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.
Keywords : Bounded operators, unbounded operators, $ell$-Köthe spaces