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Absolutely continuous linear operators on Köthe-Bochner spaces

(2011)

Banach Center Publications

Let E be a Banach function space over a finite and atomless measure space (Ω,Σ,μ) and let ( X , | | · | | X ) and ( Y , | | · | | Y ) be real Banach spaces. A linear operator T acting from the Köthe-Bochner space E(X) to Y is said to be absolutely continuous if | | T ( 1 A f ) | | Y 0 whenever μ(Aₙ) → 0, (Aₙ) ⊂ Σ. In this paper we examine absolutely continuous operators from E(X) to Y. Moreover, we establish relationships between different classes of linear operators from E(X) to Y.

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