Absolutely continuous linear operators on Köthe-Bochner spaces

Banach Center Publications, Tome 95 (2011), p. 85-89 / Harvested from The Polish Digital Mathematics Library

Résumé

Let E be a Banach function space over a finite and atomless measure space (Ω,Σ,μ) and let $(X, | | \cdot | |_{X})$ and $(Y, | | \cdot | |_{Y})$ 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 $| | T (1_{A ₙ} f) {| |}_{Y} \to 0$ 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.

Publié le : 2011-01-01

Zbl 1266.47052

EUDML-ID : urn:eudml:doc:282496

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     title = {Absolutely continuous linear operators on K\"othe-Bochner spaces},
     journal = {Banach Center Publications},
     volume = {95},
     year = {2011},
     pages = {85-89},
     zbl = {1266.47052},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-6}
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 (éd.). Absolutely continuous linear operators on Köthe-Bochner spaces. Banach Center Publications, Tome 95 (2011) pp. 85-89. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc92-0-6/