Abstract
Let (Ω, Σ, μ) be a complete σ-finite measure space, φ a Young function and X and Y be Banach spaces. Let Lφ(X) denote the corresponding Orlicz-Bochner space and
$\begin{array}{}
\displaystyle
\mathcal T^\wedge_\varphi
\end{array}$ denote the finest Lebesgue topology on Lφ(X). We examine different classes of (
$\begin{array}{}
\displaystyle
\mathcal T^\wedge_\varphi
\end{array}$, ∥ ⋅ ∥Y)-continuous linear operators T : Lφ(X) → Y: weakly compact operators, order-weakly compact operators, weakly completely continuous operators, completely continuous operators and compact operators. The relationships among these classes of operators are established.
Duality problem for the class of limited completely continuous operators
