Bounded factorization property for ℓ-Köthe spaces


Filomat, vol.37, no.11, pp.3631-3637, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 11
  • Publication Date: 2023
  • Doi Number: 10.2298/fil2311631y
  • Journal Name: Filomat
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, zbMATH
  • Page Numbers: pp.3631-3637
  • Keywords: Bounded factorization property, Locally convex spaces, Unbounded operators, ℓ-Köthe spaces
  • Middle East Technical University Affiliated: Yes


Let ℓ denote a Banach sequence space with a monotone norm in which the canonical system (en )n is an unconditional basis. We show that the existence of an unbounded continuous linear operator T between ℓ-Köthe spaces λℓ (A) and λℓ (C) which factors through a third ℓ-Köthe space λℓ (B) causes the existence of an unbounded continuous quasidiagonal operator from λℓ (A) into λℓ (C) factoring through λℓ (B) as a product of two continuous quasidiagonal operators. Using this result, we study when the triple (λℓ (A), λℓ (B), λℓ (C)) satisfies the bounded factorization property BF (which means that all continuous linear operators from λℓ (A) into λℓ (C) factoring through λℓ (B) are bounded). As another application, we observe that the existence of an unbounded factorized operator for a triple of ℓ-Köthe spaces, under some additional assumptions, causes the existence of a common basic subspace at least for two of the spaces.