HAHN-BANACH-KANTOROVICH TYPE THEOREMS WITH THE RANGE SPACE NOT NECESSARILY (O)-COMPLETE

Abstract

In the classical Hahn-Banach-Kantorovich theorem, the range space $Y$ is Dedekind complete. In this paper, by extending the arguments of the original Hahn-Banach-Kantorovich theorem and using an idea of Y. A. Abramovich and A. W. Wickstead, we can weaken the order theoretic assumption on $Y$\ and obtain more general results in the settings of Banach lattices as well as ordered linear spaces.