Dunford-Pettis operators on the space of Bochner integrable functions

Marian Nowak

Marian Nowak

Banach Center Publications, Tome 95 (2011), p. 353-358 / Harvested from The Polish Digital Mathematics Library

Résumé

Let (Ω,Σ,μ) be a finite measure space and let X be a real Banach space. Let $L^{Φ} (X)$ be the Orlicz-Bochner space defined by a Young function Φ. We study the relationships between Dunford-Pettis operators T from L¹(X) to a Banach space Y and the compactness properties of the operators T restricted to $L^{Φ} (X)$ . In particular, it is shown that if X is a reflexive Banach space, then a bounded linear operator T:L¹(X) → Y is Dunford-Pettis if and only if T restricted to $L^{\infty} (X)$ is $(τ (L^{\infty} (X), L ¹ (X *)), | | \cdot | |_{Y})$ -compact.

Publié le : 2011-01-01

Zbl 1234.47025

EUDML-ID : urn:eudml:doc:281614

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     author = {Marian Nowak},
     title = {Dunford-Pettis operators on the space of Bochner integrable functions},
     journal = {Banach Center Publications},
     volume = {95},
     year = {2011},
     pages = {353-358},
     zbl = {1234.47025},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc95-0-21}
}

Marian Nowak. Dunford-Pettis operators on the space of Bochner integrable functions. Banach Center Publications, Tome 95 (2011) pp. 353-358. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc95-0-21/