2016/04/16 by Ersin Kızgut, Kızgut, Ersin, Elif Uyanık +3
Mathematics · #46A03 #46A32 #46A45 #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #Banach space #Bounded function #Bounded operator #Combinatorics #Discrete mathematics #Domain (mathematical analysis) #FOS: Mathematics #Factorization #Functional Analysis (math.FA) #Injective function #Mathematical analysis #Mathematics #Monotone polygon #math.FA #msc:46A03 #msc:46A32 #msc:46A45
paper · pdf · doi:10.48550/arxiv.1604.05298
published in arXiv (Cornell University) (Cornell University) · Withdrawn due to an error in Theorem 2.1
openalex publication_date 2016/04/16 · arxiv created 2016/05/01 · arxiv updated 2016/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For locally convex spaces X and Y, the continuous linear map T:X → Y is said to be bounded if it maps zero neighborhoods of X into bounded sets of Y. We denote (X,Y) ∈ B when every operator between X and Y is bounded. For a Banach space ℓ with a monotone norm ‖⋅‖ in which the canonical system (en) forms an unconditional basis, we consider ℓ-Köthe spaces as a generalization of usual Köthe spaces. In this note, we characterize ℓ-Köthe spaces ℓ(apn) and ℓ(bsm) such that (ℓ(apn), ℓ(bsm)) ∈ B. A pair (X,Y) is said to have the bounded factorization property, and denoted (X,Y) ∈ BF, if each linear continuous operator T : X → X that factors over Y is bounded. We also prove that injective tensor products of some classical Köthe spaces have bounded factorization property.