## On Isometric Isomorphism Of $LUC(G)^*$
Let $G$ be a locally compact Hausdorff topological group. We can extend the notion of uniform continuity from the locally compact commutative group $mathbb{R}$ to $G$ in two ways. For non-commutative groups, right-uniform-continuity may be different from left-uniform-continuity. Let $LUC(G)$ be the Banach space of all left-uniformly-continuous functions on $G$. The dual space $LUC(G)^*$ of $LUC(G)$ can be made into a Banach algebra by an Arens type of product. In this talk first I will review some background. Then I intend to present my recent work regarding to the isometric isomorphisms of $LUC(G)^*$.