This paper concerns the positive domination property of compact operators on pre-Riesz spaces. The method is embedding the pre-Riesz space into its Riesz completion. It also involves extension of order continuous norms. The compactness of the third power of a positive operator dominated by a compact operator is obtained in a pre-Riesz space which has an order unit.

中文翻译：

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前Riesz空间上的控制性质和正紧算子的扩展

本文涉及前Riesz空间上紧算子的正控制性。该方法将前Riesz空间嵌入其Riesz完成中。它还涉及订单连续规范的扩展。在具有阶数单位的前里兹空间中，获得了由紧致算子主导的正算子的三次幂的紧致性。