ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 46, 47 Koshi, Shozo, Hokkaido Institute of Technology, Japan Partially ordered linear space Let E be a partially ordered linear space with positive cone P such that P − P = E and that the intersection of P and −P is 0. We shall consider the supremum set for a subset in E which is bounded above and shall discuss several properties for the supremum set and the distributive law. E has the distributive law if and only if E is a Riesz space. We discuss some order properties of Hermitian operators in this framework. References: Y. C. Wong, Lecture Note 531 (1976), A. C. Zaanen: Springer Verlag (1997).