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A remark on a paper of P. B. Djakov and M. S. Ramanujan
- Source :
- TURKISH JOURNAL OF MATHEMATICS. 43:2494-2498
- Publication Year :
- 2019
- Publisher :
- The Scientific and Technological Research Council of Turkey (TUBITAK-ULAKBIM) - DIGITAL COMMONS JOURNALS, 2019.
-
Abstract
- 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-K\"{o}the spaces, then there exists a continuous unbounded quasi-diagonal operator between them. Using this result, we study in terms of corresponding K\"{o}the matrices when every continuous linear operator between l-K\"{o}the spaces is bounded. As an application, we observe that the existence of an unbounded operator between l-K\"{o}the spaces, under a splitting condition, causes the existence of a common basic subspace.
Details
- ISSN :
- 13036149
- Volume :
- 43
- Database :
- OpenAIRE
- Journal :
- TURKISH JOURNAL OF MATHEMATICS
- Accession number :
- edsair.doi...........ea912feca5a2f6d9db8b9172c07ed90c