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


Uyanik E., YURDAKUL M. H.

TURKISH JOURNAL OF MATHEMATICS, vol.43, no.5, pp.2494-2498, 2019 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 5
  • Publication Date: 2019
  • Doi Number: 10.3906/mat-1905-90
  • Title of Journal : TURKISH JOURNAL OF MATHEMATICS
  • Page Numbers: pp.2494-2498

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-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.