Linear operators on non-locally convex Orlicz spaces

Marian Nowak; Agnieszka Oelke

Banach Center Publications, Tome 83 (2008), p. 157-165 / Harvested from The Polish Digital Mathematics Library

Résumé

We study linear operators from a non-locally convex Orlicz space $L^{Φ}$ to a Banach space $(X, | | \cdot | |_{X})$ . Recall that a linear operator $T : L^{Φ} \to X$ is said to be σ-smooth whenever $u ₙ ⟶^{(o)} 0$ in $L^{Φ}$ implies ${| | T (u ₙ) | |}_{X} \to 0$ . It is shown that every σ-smooth operator $T : L^{Φ} \to X$ factors through the inclusion map $j : L^{Φ} \to L^{Φ ̅}$ , where Φ̅ denotes the convex minorant of Φ. We obtain the Bochner integral representation of σ-smooth operators $T : L^{Φ} \to X$ . This extends some earlier results of J. J. Uhl concerning the Bochner integral representation of linear operators defined on a locally convex Orlicz space.

Publié le : 2008-01-01

Zbl 1145.46018

EUDML-ID : urn:eudml:doc:282076

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     author = {Marian Nowak and Agnieszka Oelke},
     title = {Linear operators on non-locally convex Orlicz spaces},
     journal = {Banach Center Publications},
     volume = {83},
     year = {2008},
     pages = {157-165},
     zbl = {1145.46018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc79-0-12}
}

Marian Nowak; Agnieszka Oelke. Linear operators on non-locally convex Orlicz spaces. Banach Center Publications, Tome 83 (2008) pp. 157-165. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc79-0-12/