Geodesic
Bounded factorization property for ℓ-Köthe spaces
Filomat, Tome 37 (2023) no. 11, p. 3631

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DOI

Let ℓ denote a Banach sequence space with a monotone norm in which the canonical system (e n) n is an unconditional basis. We show that the existence of an unbounded continuous linear operator T between ℓ-Köthe spaces λ ℓ (A) and λ ℓ (C) which factors through a third ℓ-Köthe space λ ℓ (B) causes the existence of an unbounded continuous quasidiagonal operator from λ ℓ (A) into λ ℓ (C) factoring through λ ℓ (B) as a product of two continuous quasidiagonal operators. Using this result, we study when the triple (λ ℓ (A), λ ℓ (B), λ ℓ (C)) satisfies the bounded factorization property BF (which means that all continuous linear operators from λ ℓ (A) into λ ℓ (C) factoring through λ ℓ (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.
DOI : 10.2298/FIL2311631Y
Classification : 46A45
Keywords: Locally convex spaces, Unbounded operators, ℓ-Köthe spaces, Bounded factorization property 
Hayrettin Murat Yurdakul; Emre Taştüner. Bounded factorization property for ℓ-Köthe spaces. Filomat, Tome 37 (2023) no. 11, p. 3631 . doi: 10.2298/FIL2311631Y
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     title = {Bounded factorization property for {\ensuremath{\ell}-K\"othe} spaces},
     journal = {Filomat},
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     year = {2023},
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     doi = {10.2298/FIL2311631Y},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2311631Y/}
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