Version Of Hahn-Banach Theorem Research Articles

Some new versions of Hahn-Banach theorem

In 1997, L.-G. Huang and X. Zhang introduced the cone metric space, which is the generalization of the metric space. Further, some authors introduced the cone normed space. In this paper, we introduce the conceptions of bounded linear operator from a normed space to a cone normed space and bounded linear operator between two cone normed spaces. A general Hahn-Banach type linear operator extension theorem from a linear space to a partial ordering linear space, with the order is induced by a minimal cone, is proven. Two preserved-norm bounded linear operator extension theorems, one is from a normed space to a cone normed space and another is between two cone normed spaces, and some corollaries are given.