Strongly order continuous operators on Riesz spaces
Bahramnezhad, Akbar · Azar, Kazem Haghnejad
Original · EN
In this paper we introduce two new classes of operators that we call strongly order continuous and strongly σ-order continuous operators. An operator T:E→ F between two Riesz spaces is said to be strongly order continuous (resp. strongly σ-order continuous), if x αuo0 (resp. x ₙ uo0) in E implies Tx αo0 (resp. Tx ₙ o0) in F. We give some conditions under which order continuity will be equivalent to strongly order continuity of operators on Riesz spaces. We show that the collection of all so-continuous linear functionals on a Riesz space E is a band of E.
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