An operator characterization of continuous Riesz spaces

作者：Wnuk Witold^*

来源：Indagationes Mathematicae, 2012, 23(1-2): 105-112.

DOI：10.1016/j.indag.2011.10.008

• Discrete Riesz space
• Continuous Riesz space
• Order bounded operator
• Finite rank operator

We show that the orthogonality of order bounded finite rank operators T : E -%26gt; 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).

• 出版日期2012-3