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.
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