A continuous operator T between two normed vector lattices E and F is called unbounded order-norm continuous whenever x? uo? 0 implies ||Tx?|| ? 0, for each norm bounded net (x?)? ? E. Let E and F be two Banach lattices. A continuous operator T : E ? F is called unbounded norm continuous, if for each norm bounded net (x?)? ? E, x? un? 0 implies Tx? un? 0. In this manuscript, we study some properties of these classes of operators and investigate their relationships with the other classes of operators.

No abstract

Let E be a sublattice of a vector lattice F. In this paper, we will introduce and study some properties of this new class of operators as F-order-norm continuousoperators and its relationships with some known classifications of operators. We also define the new class of operators that named order weakly compact operators. A continuous operator T : E → X is said to be F-order weakly compact, if T(A) in X is arelatively weakly compact set for each Fo-bounded A ⊆ E. In this manuscript, we study some properties of this class of operators and its relationships with F-order-norm continuous operators.

No abstract