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We study the topological properties of the space $ℒ(L^{\varphi },X)$ 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 $ℒ(L^{\varphi },X)$ with the Banach space structure. Moreover, we examine the space ${ℒ}_s(L^{\varphi },X)$ of all singular operators from $L^{\varphi }$ to $X$.

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