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The order continuous operators consider one of important topic in functional analysis and its applications, the affiliations among order continuous operators and the other classes of operators such as -order are continuous, order bounded, and singular operators, have been studied and investigated, we proved that if an order bounded operator concerning two Riesz space with Dedekind complete is continuous and ordered, then is order continuous, and this paper shows that if is space that is countable, now is not -order continuous, while is uncountable, then is necessarily -order continuous, by giving an example we showed that null ideal for the operator is band when is bounded ordered, further, it is ordered and continuous. Finally, we concluded the operator that is a positively and orderly continuous map on ordered dense with memorizing Riesz subspace of a Riesz space with its range is Dedekind complete, it has only unique ordered continuous expansion all of space.
Elzidani et al. (Fri,) studied this question.