We explore inverses of disjointness preserving bijections in infinite dimensional normed pre-Riesz spaces by several methods. As in the case of Banach lattices, our aim is to show that such inverses are disjointness preserving. One method is extension of the operator to the Riesz completion, which works under suitable denseness and continuity conditions. Another method involves a condition on principle bands. Examples illustrate the differences to the Riesz space theory.

中文翻译：

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规范的前Riesz空间上的不相交保持算符：扩展和逆

我们通过几种方法探索在无穷维赋范数的前Riesz空间中保持不相交的双射的逆。与Banach格的情况一样，我们的目的是证明这种逆是不相交的。一种方法是将运算符扩展到Riesz完井，该完井可以在适当的密度和连续性条件下进行。另一种方法涉及主频带上的条件。实例说明了与里斯空间理论的不同之处。