Volume 36 • Number 1 • 2013   • Unbounded Weighted Radon Measures and Dual of Certain Function Spaces with Strict Topology S. Maghsoudi and A. Rejali Abstract. Let $X$ be a $C$-distinguished topological space, and let $\omega$ be a weight function on $X$. Denote by $C_b(X, \omega)$ the space of all real-valued functions $f$ with $f/\omega\in C_b(X)$, and by $\widetilde{C}_b(X, \omega)$ the space of all real-valued continuous functions $f$ such that $f/\omega$ is bounded. We introduce certain locally convex topologies on $C_b(X, \omega)$ and $\widetilde{C}_b(X, \omega)$, and as our main results we determine their duals. 2010 Mathematics Subject Classification: Primary 46E10, 46E27 Secondary: 46A03, 46A40 Full text: PDF