Reflexive extended locally convex spaces

Abstract

For an extended locally convex space (elcs) $(X,\ddot{I}„)$, the authors in [10] studied the topology $\ddot{I}{„}_{ucb}$ of uniform convergence on bounded subsets of $(X,\ddot{I}„)$ on the dual $X^{\ast }$ of $(X,\ddot{I}„)$. In the present paper, we use the topology $\ddot{I}{„}_{ucb}$ to explore the reflexive property of extended locally convex spaces. It is shown that an elcs is (semi) reflexive if and only if any of its open subspaces is (semi) reflexive. For an extended normed space, we show that reflexivity is a three-space property.

17 pages