STRONGLY ORDER CONTINUOUS OPERATORS ON RIESZ SPACES.

In this paper we introduce two new classes of operators which are called strongly order continuous and order-to-unbounded order continuous operators and we study their lattice properties. With under some conditions, we show that order continuity is equivalent to strongly order continuity of operators on Riesz spaces. We show that the collection of all strongly continuous linear functionals on a Riesz space E is a band of E~. [ABSTRACT FROM AUTHOR]