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Topological properties of spaces of linear operators on non-locally convex Orlicz spaces

100%

Oelke A.

Commentationes Mathematicae

2010

tom 50

nr 2

We study the topological properties of the space $\mathcal{L}(L^\varphi, X)$ of all continuous linear operators from an Orlicz space $L^\varphi$ (an Orlicz function $\varphi$ is not necessarily convex) to a Banach space $X$. We provide the space $\mathcal{L}(L^\varphi ,X)$ with the Banach space structure. Moreover, we examine the space $\mathcal{L}_s (L^\varphi, X)$ of all singular operators from $L^\varphi$ to $X$.

Linear operators on non-locally convex Orlicz spaces

63%

Nowak M., Oelke A.

Banach Center Publications

2008

tom 79

nr 1

157-165

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

Ograniczanie wyników

1 Banach Center Publications

1 Commentationes Mathematicae

2 Oelke A.

1 Nowak M.

1 2010

1 2008

Wyniki wyszukiwania

Topological properties of spaces of linear operators on non-locally convex Orlicz spaces

Linear operators on non-locally convex Orlicz spaces