一类正交射的刻画

Characterization of a Type of Orthomorphism

给出n维欧氏空间R″按通常的偏序做成的阿基米德Riesz空间上正交射的特征,以此可对R″上序有界算子作关于正交射的直和分解。最后,构造一个反例说明,对于R″按字典顺序做成的非阿基米德Riesz空间的情形,这个刻画及相应结果并不成立。

In this paper, the orthomorphisms on the Archimedean Riesz space Rn with the usual coordinatewise ordering are characterized. Also, the decomposition of an order bounded operator with respect to the orthomorphisms is obtained . In addition, a counterexample is given to show that the characterization and the related results do not hold for the non-Archimedeam Riesz space Rn with the lexicographical ordering.