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Bounded factorization property for ℓ-Köthe spaces
Date
2023-01-01
Author
Yurdakul, Murat Hayrettin
Taştüner, Emre
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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.
Subject Keywords
Bounded factorization property
,
Locally convex spaces
,
Unbounded operators
,
ℓ-Köthe spaces
URI
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85149751359&origin=inward
https://hdl.handle.net/11511/102629
Journal
Filomat
DOI
https://doi.org/10.2298/fil2311631y
Collections
Department of Mathematics, Article
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M. H. Yurdakul and E. Taştüner, “Bounded factorization property for ℓ-Köthe spaces,”
Filomat
, vol. 37, no. 11, pp. 3631–3637, 2023, Accessed: 00, 2023. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85149751359&origin=inward.