Abstract
We show that the orthogonality of order bounded finite rank operators T : E → E to the identity operator on E is equivalent to the continuity of the space E . We also describe discrete elements in the space L b ( E , F ) of order bounded linear maps transforming a Riesz space E into a Dedekind complete Riesz space F . Our description is the same as in Wickstead (1981) [5] but we obtain it making less restrictive, more natural assumptions and presenting a different proof. Additionally, we formulate a necessary and sufficient condition for the discreteness and continuity of L b ( E , F ) .
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